{"id":64903,"date":"2025-06-20T10:36:48","date_gmt":"2025-06-20T07:36:48","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=64903"},"modified":"2026-10-26T09:49:18","modified_gmt":"2026-10-26T06:49:18","slug":"eigenvalues-eigenvectors-2x2","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/eigenvalues-eigenvectors-2x2\/","title":{"rendered":"Eigenvalue and Eigenvector Calculator \u2013 2\u00d72 Matrix"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">2\u00d72 Matrix Eigenvalues and Eigenvectors Solver<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"64903\" data-favorite-title=\"Eigenvalues and Eigenvectors 2\u00d72\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/eigenvalues-eigenvectors-2x2\/\" data-favorite-excerpt=\"Enter the four elements of a 2\u00d72 matrix to get its eigenvalues and eigenvectors, plus the determinant, trace, and characteristic polynomial with a full worked solution.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-algebra\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/mathematics\/eigenvalues-eigenvectors-2x2\/\" method=\"POST\" class=\"calculator\" id=\"calculator-64903\" data-post=\"64903\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">a\u2081\u2081<\/label><div class=\"term\">a11<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"a\" id=\"field-1\" aria-describedby=\"calc-info-1\" step=\"any\" value=\"4\"\/><small id=\"calc-info-1\">Matrix element at row 1, column 1<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">a\u2081\u2082<\/label><div class=\"term\">a12<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"a\" id=\"field-2\" aria-describedby=\"calc-info-2\" step=\"any\" value=\"2\"\/><small id=\"calc-info-2\">Matrix element at row 1, column 2<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">a\u2082\u2081<\/label><div class=\"term\">a21<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"a\" id=\"field-3\" aria-describedby=\"calc-info-3\" step=\"any\" value=\"1\"\/><small id=\"calc-info-3\">Matrix element at row 2, column 1<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">a\u2082\u2082<\/label><div class=\"term\">a22<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"a\" id=\"field-4\" aria-describedby=\"calc-info-4\" step=\"any\" value=\"3\"\/><small id=\"calc-info-4\">Matrix element at row 2, column 2<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"64903\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Your Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>|A| \u2014 Determinant of the matrix<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Trace A \u2014 Sum of diagonal elements<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-3\"><span class=\"field-title\"><span>Degenerate matrix (A \u2212 c\u00d7I)<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-4\"><span class=\"field-title\"><span>|A \u2212 c\u00d7I| \u2014 Characteristic polynomial<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-5\"><span class=\"field-title\"><span>Eigenvalue \u03bb\u2081<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-6\"><span class=\"field-title\"><span>Eigenvalue \u03bb\u2082<\/span><\/span><span class=\"field-value\" id=\"result-6\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-7\"><span class=\"field-title\"><span>Eigenvector for \u03bb\u2081 (x\u2081, x\u2082)<\/span><\/span><span class=\"field-value\" id=\"result-7\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-8\"><span class=\"field-title\"><span>Eigenvector for \u03bb\u2082 (x\u2081, x\u2082)<\/span><\/span><span class=\"field-value\" id=\"result-8\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copy link to this calculation<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"64903\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Eigenvalues and Eigenvectors Formula for 2\u00d72 Matrix<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ \\det(A - \\lambda I) = 0 \\\\ (A - \\lambda I)\\vec{v} = \\vec{0} \\\\ \\det\\begin{bmatrix} a - \\lambda &amp; b \\\\ c &amp; d - \\lambda \\end{bmatrix} = (a-\\lambda)(d-\\lambda) - bc = 0 \\\\ \\lambda_{1,2} = \\frac{\\operatorname{tr}(A) \\pm \\sqrt{\\operatorname{tr}(A)^2 - 4\\det(A)}}{2} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\( A = \\begin{bmatrix} a &amp; b \\\\ c &amp; d \\end{bmatrix} \\) \u2014 the 2\u00d72 matrix<\/li>\n<li>\\( \\lambda \\) \u2014 the eigenvalues (the roots of the characteristic equation)<\/li>\n<li>\\( \\vec{v} \\) \u2014 the corresponding eigenvectors, found by solving \\( (A - \\lambda I)\\vec{v} = \\vec{0} \\)<\/li>\n<li>\\( \\operatorname{tr}(A) = a + d \\) \u2014 the trace, and \\( \\det(A) = ad - bc \\) \u2014 the determinant<\/li>\n<\/ul>\n<p>The first equation defines the characteristic polynomial \\( \\lambda^2 - \\operatorname{tr}(A)\\lambda + \\det(A) = 0 \\). Solving it (a simple quadratic) gives both eigenvalues, and each eigenvalue then yields an eigenvector from the homogeneous system \\( (A - \\lambda I)\\vec{v} = \\vec{0} \\).<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-459\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Eigenvalues and Eigenvectors 2\u00d72 \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> find the eigenvalues and eigenvectors of the matrix<\/p>\n<p>\\[ A = \\begin{bmatrix} 4 &amp; 2 \\\\ 1 &amp; 3 \\end{bmatrix} \\]<\/p>\n<p>Step 1 \u2014 trace and determinant: \\( \\operatorname{tr}(A) = 4 + 3 = 7 \\), \\( \\det(A) = 4 \\cdot 3 - 2 \\cdot 1 = 10 \\).<\/p>\n<p>Step 2 \u2014 characteristic equation: \\( \\lambda^2 - 7\\lambda + 10 = 0 \\).<\/p>\n<p>\\[ \\lambda_{1,2} = \\frac{7 \\pm \\sqrt{49 - 40}}{2} = \\frac{7 \\pm 3}{2} \\]<\/p>\n<p>Step 3 \u2014 eigenvalues: \\( \\lambda_1 = 5 \\), \\( \\lambda_2 = 2 \\).<\/p>\n<p>Step 4 \u2014 eigenvectors from \\( (A - \\lambda I)\\vec{v} = \\vec{0} \\). For \\( \\lambda_1 = 5 \\): \\( (4-5)x_1 + 2x_2 = 0 \\), so \\( x_2 = 0.5x_1 \\) and \\( \\vec{v}_1 = (1,\\ 0.5) \\). For \\( \\lambda_2 = 2 \\): \\( (4-2)x_1 + 2x_2 = 0 \\), so \\( x_2 = -x_1 \\) and \\( \\vec{v}_2 = (1,\\ -1) \\).<\/p>\n<p><strong>Result:<\/strong> \\( \\lambda_1 = 5 \\) with eigenvector \\( (1,\\ 0.5) \\); \\( \\lambda_2 = 2 \\) with eigenvector \\( (1,\\ -1) \\). Verification: \\( A\\vec{v}_1 = (5,\\ 2.5) = 5\\vec{v}_1 \\) and \\( A\\vec{v}_2 = (2,\\ -2) = 2\\vec{v}_2 \\).<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Eigenvalue Calculator<\/h2>\n<ol>\n<li>Enter the matrix element <strong>a\u2081\u2081<\/strong> (row 1, column 1). The default value is 4.<\/li>\n<li>Enter <strong>a\u2081\u2082<\/strong> (row 1, column 2). The default value is 2.<\/li>\n<li>Enter <strong>a\u2082\u2081<\/strong> (row 2, column 1). The default value is 1.<\/li>\n<li>Enter <strong>a\u2082\u2082<\/strong> (row 2, column 2). The default value is 3.<\/li>\n<li>Read the results: the determinant |A|, the trace, the matrix \\( A - cI \\), the characteristic polynomial, both eigenvalues, and the eigenvector for each eigenvalue.<\/li>\n<\/ol>\n<h2>What Are Eigenvalues and Eigenvectors?<\/h2>\n<p>An eigenvector of a matrix \\( A \\) is a nonzero vector that does not change direction when the matrix is applied to it \u2014 it is only stretched or compressed. The scaling factor of that stretch is the eigenvalue \\( \\lambda \\). Formally, \\( \\vec{v} \\) is an eigenvector if it satisfies<\/p>\n<p>\\[ A\\vec{v} = \\lambda\\vec{v} \\]<\/p>\n<p>Geometrically, a 2\u00d72 matrix transforms the plane: it rotates, stretches, and shears vectors. Most vectors end up pointing somewhere new, but up to two special directions survive the transformation unchanged (apart from scaling). Those directions are the eigenvectors, and their scaling factors are the eigenvalues. This is why eigen decomposition reveals the \"essential\" behavior of a transformation, stripping away everything else.<\/p>\n<p>Eigenvalues encode a great deal of information in just two numbers. Their product equals the determinant (how the matrix scales areas), and their sum equals the trace. If both eigenvalues are real and positive, the transformation stretches space in both eigen-directions; if one is negative, one direction is flipped; if both have absolute value less than 1, the transformation shrinks space. When both eigenvalues are equal, the matrix may or may not have two independent eigenvectors \u2014 this is the distinction between diagonalizable and defective matrices.<\/p>\n<p>Eigenvalues and eigenvectors appear everywhere in applied mathematics: stability analysis of differential equations and dynamical systems, principal component analysis in statistics, vibration modes in mechanical engineering, quantum mechanics (where eigenvalues are the measurable values of observables), and page-rank style algorithms. Where a matrix repeats its action many times \u2014 \\( A^n \\) \u2014 the largest eigenvalue dominates the long-term behavior.<\/p>\n<h2>Assumptions and Limitations<\/h2>\n<ul>\n<li><strong>Real eigenvalues only.<\/strong> The calculator solves the characteristic quadratic over the real numbers. If the discriminant \\( \\operatorname{tr}(A)^2 - 4\\det(A) &lt; 0 \\), the eigenvalues are complex and the tool reports &quot;No real roots&quot;. This happens, for example, for rotation matrices.<\/li>\n<li><strong>Eigenvectors are not unique.<\/strong> Any nonzero multiple of an eigenvector is also an eigenvector. The calculator fixes \\( x_1 = 1 \\) and reports \\( (1,\\ x_2) \\); the same direction could equally be written as \\( (2,\\ 2x_2) \\) or with opposite sign. Only the direction matters.<\/li>\n<li><strong>Repeated eigenvalues.<\/strong> When the discriminant is zero, \\( \\lambda_1 = \\lambda_2 \\) and there may be only one independent eigenvector (a defective matrix). The calculator will return the same eigenvector twice in that case.<\/li>\n<li><strong>Zero rows.<\/strong> If both \\( a_{12} \\) and \\( a_{21} \\) are zero (a diagonal matrix), the eigenvalues are simply the diagonal entries \\( a_{11} \\) and \\( a_{22} \\), and the eigenvectors fall back to the standard basis directions.<\/li>\n<li><strong>Rounding.<\/strong> Results are rounded to 4 decimal places, which is sufficient for most textbook problems but may hide small values in ill-conditioned matrices.<\/li>\n<\/ul>\n<p>To work with larger matrices, try the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/eigenvalues-eigenvectors-3x3\/\">Eigenvalues and Eigenvectors 3\u00d73 Calculator<\/a>. If you need other matrix operations first, the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/matrix-multiplication\/\">Matrix Multiplication Calculator<\/a> and the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/determinant-multiplication\/\">Determinant Multiplication Calculator<\/a> are useful companions, since eigenvalues are often computed from matrix powers and products of determinants.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Enter the four elements of a 2\u00d72 matrix to get its eigenvalues and eigenvectors, plus the determinant, trace, and characteristic polynomial with a full worked solution.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[7],"tags":[69],"class_list":["post-64903","post","type-post","status-publish","format-standard","hentry","category-mathematics","tag-matrix"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64903","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=64903"}],"version-history":[{"count":5,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64903\/revisions"}],"predecessor-version":[{"id":67548,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64903\/revisions\/67548"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=64903"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=64903"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=64903"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}