{"id":10669,"date":"2026-04-05T12:19:31","date_gmt":"2026-04-05T12:19:31","guid":{"rendered":"https:\/\/www.vedprep.com\/exams\/?p=10669"},"modified":"2026-04-05T12:19:31","modified_gmt":"2026-04-05T12:19:31","slug":"normed-linear-spaces-for-csir-net","status":"publish","type":"post","link":"https:\/\/www.vedprep.com\/exams\/csir-net\/normed-linear-spaces-for-csir-net\/","title":{"rendered":"Understanding Normed Linear Spaces : A Comprehensive guide For CSIR NET and Beyond 2026"},"content":{"rendered":"<p>Normed linear spaces are essential for CSIR NET, IIT JAM, and GATE, as they provide a framework for understanding linear functional analysis, critical for solving problems in mathematics, physics, and engineering.<\/p>\n<h2>Normed linear Spaces over C and R &#8211; Syllabus and Key Textbooks For Normed linear<\/h2>\n<p><strong>Normed Linear Spaces <\/strong>belong to Unit 6: Linear Functional Analysis in the official CSIR NET Mathematics syllabus. The unit covers various aspects of functional analysis, including <strong>normed linear spaces<\/strong>.<\/p>\n<p>A <em>normed linear space <\/em>is a vector space equipped with a norm, which assigns a non-negative real number to each element, satisfying certain properties. Students preparing for CSIR NET, IIT JAM, and GATE exams need to study this topic thoroughly, especially <strong>Normed linear Spaces For CSIR NET<\/strong>.<\/p>\n<p>The following textbooks provide in-depth coverage of normed linear, a critical aspect of <strong>Normed linear Spaces For CSIR NET<\/strong>:<\/p>\n<ul>\n<li><code>Functional Analysis<\/code> by Walter Rudin<\/li>\n<li><code>Linear Functional Analysis<\/code> by Kosaku Yosida<\/li>\n<\/ul>\n<p>These textbooks offer a full understanding of normed linear, which is essential for <strong>Normed linear <\/strong>and other related exams. Students can refer to these books to gain a deeper understanding of the concepts and theorems related to normed linear spaces, specifically <strong>Normed linear<\/strong>.<\/p>\n<h2>Defining Normed linear Spaces For CSIR NET &#8211; Core Concept of Normed linear<\/h2>\n<p>A <strong>normed linear space <\/strong>is a <em>vector space <\/em>equipped with a <strong>norm<\/strong>, which is a function that assigns a non-negative real number to each vector in the space. The norm is denoted by $\\| \\cdot \\|$ and represents the magnitude or length of a vector, a fundamental concept in <strong>Normed linear<\/strong>.<\/p>\n<p>The norm must satisfy three fundamental properties. These properties are:<\/p>\n<ul>\n<li><strong>Positivity<\/strong>: $\\|x\\| \\geq 0$ for all $x$ in the vector space, and $\\|x\\| = 0$ if and only if $x = 0$, a property required for <strong>Normed linear Spaces For CSIR NET<\/strong>.<\/li>\n<li><strong>Homogeneity<\/strong>: $\\|\\alpha x\\| = |\\alpha| \\|x\\|$ for all $x$ in the vector space and all scalars $\\alpha$, related to <strong>Normed linear Spaces For CSIR NET<\/strong>.<\/li>\n<li><strong>Triangle Inequality<\/strong>: $\\|x + y\\| \\leq \\|x\\| + \\|y\\|$ for all $x$ and $y$ in the vector space, essential for understanding <strong>Normed linear Spaces For CSIR NET<\/strong>.<\/li>\n<\/ul>\n<p>These properties ensure that the norm behaves consistently and provides a meaningful measure of vector magnitude, particularly in <strong>Normed linear Spaces For CSIR NET<\/strong>.<\/p>\n<p>Normed linear are essential in various mathematical and analytical contexts, particularly in <em>functional analysis <\/em>and <strong>Normed linear<\/strong>. Understanding these spaces is critical for students preparing for exams like CSIR NET, as they form the foundation for more advanced topics, specifically <strong>Normed linear Spaces For CSIR NET<\/strong>. A solid grasp of normed linear and their properties is vital for success in <strong>Normed linear Spaces For CSIR NET <\/strong>and other related areas of study.<\/p>\n<h2>Understanding Norms in <code>Normed linear Spaces For CSIR NET<\/code><\/h2>\n<p>The concept of normed linear is fundamental in functional analysis, particularly for students preparing for <code>Normed linear<\/code> and other competitive exams. A normed linear space, also known as a normed vector space, is a vector space where each element is associated with a scalar value called its norm, a key concept in <strong>Normed linear<\/strong>. The <strong>norm <\/strong>of a vector is a measure of its size or magnitude, crucial in <strong>Normed linear Spaces For CSIR NET<\/strong>.<\/p>\n<p>The norm must satisfy three essential properties. Firstly, it must be <strong>positive<\/strong>, meaning that the norm of a non-zero vector is always greater than zero, a property of <strong>Normed linear<\/strong>. Secondly, it must be <strong>homogeneous<\/strong>, implying that the norm of a scaled vector is equal to the scalar times the norm of the original vector, related to <strong>Normed linear Spaces For CSIR NET<\/strong>.<\/p>\n<p>Last, the norm must satisfy the <strong>triangle inequality<\/strong>, which states that the norm of the sum of two vectors is less than or equal to the sum of their individual norms, a fundamental property in <strong>Normed linear<\/strong>. Mathematically, this can be expressed as: <code>||x + y|| \u2264 ||x|| + ||y||<\/code>, where <code>x<\/code> and <code>y<\/code> are vectors in the normed linear space, essential for <strong>Normed linear<\/strong>. These properties ensure that the norm provides a well-defined measure of the size of vectors in the space, particularly for <strong>Normed linear Spaces For CSIR NET<\/strong>.<\/p>\n<h2>Worked Example: Distance Between Two Vectors in<em>Normed linear Spaces For CSIR NET<\/em><\/h2>\n<p>Consider two vectors <code>u = (1, 2)<\/code> and <code>v = (4, 6)<\/code> in the normed linear space <code>\u211d\u00b2<\/code> with the Euclidean norm, an example relevant to <strong>Normed linear<\/strong>. The distance between <code>u<\/code> and <code>v<\/code> is defined as <code>||u - v||<\/code>.<\/p>\n<p>The vector <code>u - v<\/code> is given by <code>(1 - 4, 2 - 6) = (-3, -4)<\/code>. The Euclidean norm of <code>u - v<\/code> is <code>||u - v|| = \u221a((-3)\u00b2 + (-4)\u00b2) = \u221a(9 + 16) = \u221a25 = 5<\/code>, a calculation used in <strong>Normed linear Spaces For CSIR NET<\/strong>.<\/p>\n<p>The triangle inequality states that for any vectors<code>x<\/code>and<code>y<\/code>in a normed linear space, <code>||x + y|| \u2264 ||x|| + ||y||<\/code>, a property applied in <strong>Normed linear<\/strong>. This implies that the distance between two vectors is non-negative. In this case,<code>||u - v|| = 5 \u2265 0<\/code>, which is indeed non-negative, demonstrating a concept in <strong>Normed linear Spaces For CSIR NET<\/strong>.<\/p>\n<p>This example illustrates how to find the distance between two vectors in a <em>normed linear space <\/em>and verifies that the distance satisfies the non-negativity property using the triangle inequality, a fundamental concept in <em>Normed linear <\/em>and <strong>Normed linear Spaces For CSIR NET<\/strong>.<\/p>\n<h2>Common Misconceptions About Normed linear Spaces For CSIR NET<\/h2>\n<p>Students often confuse the norm of a vector with its absolute value, a mistake to avoid in <strong>Normed linear<\/strong>. This misconception arises when considering vectors in <em>\u211d<\/em>, where the absolute value of a real number <code>x<\/code> is denoted by <code>|x|<\/code>. However, the norm of a vector <strong>x <\/strong>in a normed linear space is a generalization of the concept of length or magnitude, critical for <strong>Normed linear Spaces For CSIR NET<\/strong>.<\/p>\n<p>The norm, denoted by <code>||x||<\/code>, is not just the absolute value of the vector, but a function that assigns a non-negative real number to each vector in the space, satisfying certain properties, specifically in <strong>Normed linear Spaces For CSIR NET<\/strong>. Specifically, the norm must satisfy:<\/p>\n<ul>\n<li><strong>Positivity<\/strong>: <code>||x|| \u2265 0<\/code> for all<strong>x<\/strong>, and <code>||x|| = 0<\/code> if and only if <strong>x <\/strong>is the zero vector, a property of <strong>Normed linear<\/strong>.<\/li>\n<li><strong>Homogeneity<\/strong>: <code>||\u03b1x|| = |\u03b1| ||x||<\/code> for all scalars <code>\u03b1<\/code> and vectors <strong>x<\/strong>, related to <strong>Normed linear<\/strong>.<\/li>\n<li><strong>Triangle Inequality<\/strong>: <code>||x + y|| \u2264 ||x|| + ||y||<\/code> for all vectors <strong>x <\/strong>and <strong>y<\/strong>, essential for <strong>Normed linear<\/strong>.<\/li>\n<\/ul>\n<p>Understanding these properties is essential for working with <em>Normed linear For CSIR NET <\/em>problems, especially <strong>Normed linear<\/strong>. A normed linear space, also known as a normed vector space, is a vector space where each vector has a norm, or length, associated with it, a concept used in <strong>Normed linear Spaces For CSIR NET<\/strong>. The norm provides a way to measure the size of vectors in the space, particularly in <strong>Normed linear Spaces For CSIR NET<\/strong>.<\/p>\n<h2>Applications of<strong>Normed linear Spaces For CSIR NET<\/strong>in Physics and Engineering<\/h2>\n<p>Normed linear spaces describing the behavior of physical systems, particularly in the study of vibrations and signal processing, areas where <strong>Normed linear <\/strong>is applied. A normed linear space, also known as a <em>normed vector space<\/em>, is a vector space where each element has a scalar value associated with it, known as its <em>norm<\/em>or <em>length<\/em>, a concept from <strong>Normed linear<\/strong>. This norm can be used to measure the size or magnitude of a physical quantity, a key aspect of <strong>Normed linear Spaces For CSIR NET<\/strong>.<\/p>\n<p>In the field of signal processing, normed linear spaces are used to analyze and process signals, utilizing concepts from <strong>Normed linear<\/strong>. For instance, in audio signal processing, the norm of a signal can be used to measure its amplitude or energy, a technique based on <strong>Normed linear<\/strong>. This is achieved by defining a norm, such as the<code>L2<\/code>norm, which calculates the magnitude of a signal, a method used in <strong>Normed linear Spaces For CSIR NET<\/strong>. The <code>L2<\/code> norm is commonly used in many applications, including audio compression and image processing, all related to <strong>Normed linear Spaces For CSIR NET<\/strong>.<\/p>\n<p>Some key applications of\u00a0 normed linear spaces include:<\/p>\n<ul>\n<li>Image and signal processing, areas utilizing <strong>Normed linear Spaces For CSIR NET<\/strong><\/li>\n<li>Vibration analysis, a field applying <strong>Normed linear Spaces For CSIR NET<\/strong><\/li>\n<li>Control systems, which rely on <strong>Normed linear Spaces For CSIR NET<\/strong><\/li>\n<li>Optimization problems, solved using <strong>Normed linear Spaces For CSIR NET<\/strong><\/li>\n<\/ul>\n<p>These applications operate under constraints such as ensuring stability, minimizing errors, and optimizing performance, all of which involve <strong>Normed linear<\/strong>. Normed linear provide a powerful tool for analyzing and solving problems in these fields, making them an essential concept for students preparing for the CSIR NET exam, specifically <strong>Normed linear Spaces For CSIR NET<\/strong>.<\/p>\n<h2>Exam Strategy for CSIR NET, IIT JAM, and GATE &#8211; Focus on Normed Linear Spaces and<strong>Normed linear Spaces For CSIR NET<\/strong><\/h2>\n<p>Normed linear spaces are a fundamental concept in functional analysis, and a strong grasp of this topic, especially <strong>Normed linear <\/strong>, is essential for success in <a href=\"https:\/\/csirnet.nta.nic.in\/\" rel=\"nofollow noopener\" target=\"_blank\">CSIR NET<\/a>, IIT JAM, and GATE exams. A <em>normed linear space<\/em>is a vector space equipped with a <em>norm<\/em>, which assigns a non-negative real number to each vector, representing its magnitude or length, a key concept in <strong>Normed linear Spaces For CSIR NET<\/strong>. Understanding the definition and properties of normed linear, specifically <strong>Normed linear Spaces For CSIR NET<\/strong>, is crucial.<\/p>\n<p>The most frequently tested subtopics in normed linear spaces include the definition and properties of norms,<em>Banach spaces<\/em>, and <em>Hilbert spaces<\/em>, all relevant to <strong>Normed linear<\/strong>. To prepare for these topics, students should focus on understanding the axioms of a norm and how to work with different types of norms, such as the Euclidean norm and the <code>L^p<\/code> norm, in the context of <strong>Normed linear Spaces For CSIR NET<\/strong>.<\/p>\n<p>To master normed linear spaces, students should practice solving problems involving norms and distance between vectors, specifically in <strong>Normed linear Spaces For CSIR NET<\/strong>. This can be achieved by working through a variety of practice problems and previous years&#8217; questions from CSIR NET, IIT JAM, and GATE exams, all of which cover <strong>Normed linear<\/strong>. <a href=\"https:\/\/www.vedprep.com\/\">VedPrep<\/a> offers expert guidance and comprehensive study materials to help students prepare for <strong>Normed linear Spaces For CSIR NET<\/strong>and other topics in functional analysis.<\/p>\n<ul>\n<li>Focus on understanding the definition and properties of normed linear spaces, especially <strong>Normed linear Spaces For CSIR NET<\/strong><\/li>\n<li>Practice solving problems involving norms and distance between vectors in <strong>Normed linear.<\/strong><\/li>\n<\/ul>\n<p>By following a focused study plan and utilizing resources like VedPrep, students can develop a deep understanding of normed linear, particularly <strong>Normed linear<\/strong>, and improve their chances of success in these competitive exams.<\/p>\n<h2>Tips for Solving CSIR NET, IIT JAM, and GATE Problems Involving Normed Linear Spaces and<strong>Normed linear Spaces For CSIR NET<\/strong><\/h2>\n<p>Normed linear spaces are a crucial concept in functional analysis, frequently tested in exams like CSIR NET, IIT JAM, and GATE, and are central to <strong>Normed linear<\/strong>. A <strong>normed linear space <\/strong>is a vector space equipped with a <em>norm<\/em>, which assigns a non-negative real number to each vector, representing its magnitude or length, a key concept in <strong>Normed linear<\/strong>.<\/p>\n<p>When solving problems involving normed linear , students should first use the <strong>properties of the norm <\/strong>to simplify the problem, specifically in <strong>Normed linear<\/strong>. This includes using the homogeneity, triangle inequality, and non-negativity properties to manipulate the given expressions, all of which are essential for <strong>Normed linear<\/strong>. By applying these properties, complex problems can often be reduced to more manageable forms, particularly in <strong>Normed linear Spaces For CSIR NET<\/strong>.<\/p>\n<p>Another effective approach is to <strong>visualize the problem <\/strong>in terms of the normed linear space, a technique useful for <strong>Normed linear<\/strong>. This involves understanding the geometric interpretation of the norm and using it to analyze the given problem, specifically for <strong>Normed linear <\/strong>. VedPrep provides expert guidance on these topics, helping students to develop a deep understanding of <em>Normed linear For CSIR NET <\/em>and other related concepts.<\/p>\n<p>Some frequently tested subtopics include:<\/p>\n<ul>\n<li>Definition and properties of normed linear, especially <strong>Normed linear .<\/strong><\/li>\n<li>Examples of normed linear, such as <code>L^p<\/code> spaces, relevant to <strong>Normed linear<\/strong><\/li>\n<li>Normed linear space isomorphism, a concept in <strong>Normed linear<\/strong><\/li>\n<\/ul>\n<p>Students can master these topics and improve their problem-solving skills with focused study and practice, particularly in <strong>Normed linear<\/strong>.<\/p>\n<h2>Real-World Applications of Normed Linear Spaces &#8211; A Case Study For <strong>Normed linear<\/strong><\/h2>\n<p>Normed linear spaces signal processing and image analysis, areas where <strong>Normed linear For CSIR NET <\/strong>is applied. In these fields, the norm is used to measure the size or magnitude of a signal or image, a concept from <strong>Normed linear<\/strong>. For instance, in image denoising, a common goal is to minimize the <strong>norm <\/strong>of the difference between the original and denoised images, utilizing <strong>Normed linear For CSIR NET<\/strong>.<\/p>\n<p class=\"responsive-video-wrap clr\"><iframe title=\"Rank Booster Program | Real Analysis | Linear Algebra | CSIR NET | IIT JAM | GATE | Maths Academy\" width=\"1200\" height=\"675\" src=\"https:\/\/www.youtube.com\/embed\/rBwWHtinCV8?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<section class=\"vedprep-faq\">\n<h2>Frequently Asked Questions<\/h2>\n<h3>Core Understanding<\/h3>\n<div class=\"faq-item\">\n<h4>What is a normed linear space?<\/h4>\n<p>A normed linear space, also known as a normed vector space, is a vector space where each element has a scalar value associated with it, known as its norm, which satisfies certain properties.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>What are the properties of a norm?<\/h4>\n<p>The properties of a norm include positivity, homogeneity, and triangle inequality. These properties ensure that the norm behaves like a distance function.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>What is the difference between a normed space and a metric space?<\/h4>\n<p>A normed space is a special type of metric space where the metric is induced by a norm. Not all metric spaces have a norm.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>Can a vector space have multiple norms?<\/h4>\n<p>Yes, a vector space can have multiple norms, but they must satisfy the properties of a norm. Different norms can induce different topologies on the same vector space.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>What is an example of a normed linear space?<\/h4>\n<p>The space of all continuous functions on a closed interval with the supremum norm is an example of a normed linear space.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>What is a Banach space?<\/h4>\n<p>A Banach space is a complete normed linear space, meaning that every Cauchy sequence in the space converges to an element in the space.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>What is a Hilbert space?<\/h4>\n<p>A Hilbert space is a complete inner product space, which is a special type of normed linear space where the norm is induced by an inner product.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>What is the significance of normed linear spaces in mathematics?<\/h4>\n<p>Normed linear play a significant role in mathematics, particularly in functional analysis, operator theory, and other areas, as they provide a framework for studying linear structures with a notion of size or length.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>Can a normed linear space be finite-dimensional?<\/h4>\n<p>Yes, a normed linear space can be finite-dimensional. In fact, many finite-dimensional vector spaces can be equipped with a norm.<\/p>\n<\/div>\n<h3>Exam Application<\/h3>\n<div class=\"faq-item\">\n<h4>How are normed linear spaces used in CSIR NET?<\/h4>\n<p>Normed linear are a crucial topic in CSIR NET, particularly in the mathematics and physics sections. Questions often involve identifying properties of normed spaces or applying them to solve problems.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>What type of questions can I expect on normed linear spaces in CSIR NET?<\/h4>\n<p>You can expect questions on definitions, properties, and applications of normed linear, as well as their relationship to other mathematical concepts like linear algebra and analysis.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>How do I approach problems on normed linear spaces in CSIR NET?<\/h4>\n<p>To approach problems on normed linear, focus on understanding the definitions and properties of norms, and practice applying them to different situations.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>Can I use normed linear spaces to solve problems in physics?<\/h4>\n<p>Yes, normed linear have applications in physics, particularly in quantum mechanics and signal processing, where they are used to model and analyze physical systems.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>How can I use normed linear spaces to solve problems in CSIR NET mathematics?<\/h4>\n<p>To solve problems in CSIR NET mathematics using normed linear, focus on applying definitions, properties, and theorems related to normed spaces to different mathematical contexts.<\/p>\n<\/div>\n<h3>Common Mistakes<\/h3>\n<div class=\"faq-item\">\n<h4>What are common mistakes when working with normed linear spaces?<\/h4>\n<p>Common mistakes include confusing the properties of a norm, not checking for positivity, homogeneity, and triangle inequality, and misapplying norms to solve problems.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>How can I avoid mistakes when solving problems on normed linear spaces?<\/h4>\n<p>To avoid mistakes, carefully read the problem, identify the relevant concepts and properties, and double-check your calculations.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>What are some common misconceptions about normed linear spaces?<\/h4>\n<p>Common misconceptions include thinking that all normed spaces are complete or that the norm is always induced by an inner product.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>How can I distinguish between different types of normed linear spaces?<\/h4>\n<p>To distinguish between different types of normed linear, focus on their properties, such as completeness, and the relationships between them.<\/p>\n<\/div>\n<h3>Advanced Concepts<\/h3>\n<div class=\"faq-item\">\n<h4>What are some advanced topics related to normed linear spaces?<\/h4>\n<p>Advanced topics related to normed linear include Banach spaces, Hilbert spaces, and operator theory, which are crucial in functional analysis and other areas of mathematics.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>How do normed linear spaces relate to linear algebra and analysis?<\/h4>\n<p>Normed linear combine concepts from linear algebra, such as vector spaces and linear transformations, with analysis, particularly the study of limits and continuity.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>How do normed linear spaces relate to operator theory?<\/h4>\n<p>Operator theory is a branch of mathematics that studies linear operators between normed linear, which is crucial in functional analysis and other areas of mathematics.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>What are some current research areas related to normed linear ?<\/h4>\n<p>Current research areas related to normed linear include the study of Banach spaces, Hilbert spaces, and operator theory, as well as their applications in physics, engineering, and other fields.<\/p>\n<\/div>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>Normed linear spaces are essential for CSIR NET, IIT JAM, and GATE exams as they provide a framework for understanding linear functional analysis. This knowledge is critical for solving problems in mathematics, physics, and engineering.<\/p>\n","protected":false},"author":12,"featured_media":10668,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":"","rank_math_seo_score":90},"categories":[29],"tags":[2923,5766,5767,5768,5769,2922],"class_list":["post-10669","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-csir-net","tag-competitive-exams","tag-normed-linear-spaces-for-csir-net","tag-normed-linear-spaces-for-csir-net-notes","tag-normed-linear-spaces-for-csir-net-questions","tag-normed-linear-spaces-for-csir-net-study-material","tag-vedprep","entry","has-media"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/posts\/10669","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/comments?post=10669"}],"version-history":[{"count":2,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/posts\/10669\/revisions"}],"predecessor-version":[{"id":11993,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/posts\/10669\/revisions\/11993"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/media\/10668"}],"wp:attachment":[{"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/media?parent=10669"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/categories?post=10669"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/tags?post=10669"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}