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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Matrix and Vector Types · QEDcore.jl</title><meta name="title" content="Matrix and Vector Types · QEDcore.jl"/><meta property="og:title" content="Matrix and Vector Types · QEDcore.jl"/><meta property="twitter:title" content="Matrix and Vector Types · QEDcore.jl"/><meta name="description" content="Documentation for QEDcore.jl."/><meta property="og:description" content="Documentation for QEDcore.jl."/><meta property="twitter:description" content="Documentation for QEDcore.jl."/><meta property="og:url" content="https://qedjl-project.gitlab.io/QEDcore.jl/generated/vectors/"/><meta property="twitter:url" content="https://qedjl-project.gitlab.io/QEDcore.jl/generated/vectors/"/><link rel="canonical" href="https://qedjl-project.gitlab.io/QEDcore.jl/generated/vectors/"/><script data-outdated-warner src="../../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../search_index.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/catppuccin-mocha.css" data-theme-name="catppuccin-mocha"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/catppuccin-macchiato.css" data-theme-name="catppuccin-macchiato"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/catppuccin-frappe.css" data-theme-name="catppuccin-frappe"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/catppuccin-latte.css" data-theme-name="catppuccin-latte"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../../">QEDcore.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><span class="tocitem">Tutorials</span><ul><li><a class="tocitem" href="../ps_def/">Phase Space Definitions</a></li><li><a class="tocitem" href="../particles/">Particles and Phase Space Points</a></li><li class="is-active"><a class="tocitem" href>Matrix and Vector Types</a><ul class="internal"><li><a class="tocitem" href="#Lorentz-Vectors"><span>Lorentz Vectors</span></a></li><li><a class="tocitem" href="#Bispinors-and-Adjoint-Bispinors"><span>Bispinors and Adjoint Bispinors</span></a></li><li><a class="tocitem" href="#Dirac-and-Gamma-Matrices"><span>Dirac and Gamma Matrices</span></a></li></ul></li></ul></li><li><span class="tocitem">API reference</span><ul><li><a class="tocitem" href="../../library/outline/">Contents</a></li><li><a class="tocitem" href="../../library/particles/">Particles</a></li><li><a class="tocitem" href="../../library/coordinates/">Coordinates</a></li><li><a class="tocitem" href="../../library/phasespacedef/">Phase Space Definition</a></li><li><a class="tocitem" href="../../library/phase_space_layout/">Phase Space Layout</a></li><li><a class="tocitem" href="../../library/phasespacepoint/">Phase Space Points</a></li><li><a class="tocitem" href="../../library/vectors/">Vector Types</a></li><li><a class="tocitem" href="../../library/lorentzboosts/">Lorentz Boosts</a></li><li><a class="tocitem" href="../../library/">Index</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Tutorials</a></li><li class="is-active"><a href>Matrix and Vector Types</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Matrix and Vector Types</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/QEDjl-project/QEDcore.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/QEDjl-project/QEDcore.jl/blob/dev/docs/src/tutorial/vectors.jl" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Vector-and-Matrix-Types"><a class="docs-heading-anchor" href="#Vector-and-Matrix-Types">Vector and Matrix Types</a><a id="Vector-and-Matrix-Types-1"></a><a class="docs-heading-anchor-permalink" href="#Vector-and-Matrix-Types" title="Permalink"></a></h1><p><strong>TBW</strong></p><pre><code class="language-julia hljs">using QEDcore</code></pre><h2 id="Lorentz-Vectors"><a class="docs-heading-anchor" href="#Lorentz-Vectors">Lorentz Vectors</a><a id="Lorentz-Vectors-1"></a><a class="docs-heading-anchor-permalink" href="#Lorentz-Vectors" title="Permalink"></a></h2><pre><code class="language-julia hljs">lv = rand(SLorentzVector)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">4-element SLorentzVector{Float64} with indices SOneTo(4): | ||
0.24236444121334033 | ||
0.6391376857319616 | ||
0.3579473250987263 | ||
0.9812629152538076</code></pre><h2 id="Bispinors-and-Adjoint-Bispinors"><a class="docs-heading-anchor" href="#Bispinors-and-Adjoint-Bispinors">Bispinors and Adjoint Bispinors</a><a id="Bispinors-and-Adjoint-Bispinors-1"></a><a class="docs-heading-anchor-permalink" href="#Bispinors-and-Adjoint-Bispinors" title="Permalink"></a></h2><pre><code class="language-julia hljs">bs = rand(BiSpinor)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">4-element BiSpinor with indices SOneTo(4): | ||
0.16266343171463282 + 0.39781276020471723im | ||
0.3898703179615076 + 0.688697530851377im | ||
0.5014835390364512 + 0.9574848949667961im | ||
0.7610115114949229 + 0.3190012400616381im</code></pre><pre><code class="language-julia hljs">abs = rand(AdjointBiSpinor)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">4-element AdjointBiSpinor with indices SOneTo(4): | ||
0.041562058618322184 + 0.1831831618083677im | ||
0.35851068252673857 + 0.5999598935299681im | ||
0.07970829118397527 + 0.7920997675829757im | ||
0.9183822435413531 + 0.026482217648545303im</code></pre><pre><code class="language-julia hljs">abs * bs</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">-0.3675297634285666 + 1.313805921835989im</code></pre><h2 id="Dirac-and-Gamma-Matrices"><a class="docs-heading-anchor" href="#Dirac-and-Gamma-Matrices">Dirac and Gamma Matrices</a><a id="Dirac-and-Gamma-Matrices-1"></a><a class="docs-heading-anchor-permalink" href="#Dirac-and-Gamma-Matrices" title="Permalink"></a></h2><pre><code class="language-julia hljs">gm = rand(DiracMatrix)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">4×4 DiracMatrix with indices SOneTo(4)×SOneTo(4): | ||
0.951955+0.680856im 0.367873+0.147163im … 0.670667+0.645976im | ||
0.835196+0.0355848im 0.84511+0.658165im 0.525778+0.636683im | ||
0.66869+0.214142im 0.166647+0.954917im 0.556827+0.983779im | ||
0.170725+0.280409im 0.681167+0.779661im 0.49302+0.404638im</code></pre><pre><code class="language-julia hljs">abs * gm * bs</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">-4.5053780090021505 + 3.180583672697105im</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../particles/">« Particles and Phase Space Points</a><a class="docs-footer-nextpage" href="../../library/outline/">Contents »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Tuesday 5 November 2024 22:20">Tuesday 5 November 2024</span>. Using Julia version 1.10.6.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> | ||
0.6898706730059716 | ||
0.9497200121094976 | ||
0.7347703761179765 | ||
0.06971625539356274</code></pre><h2 id="Bispinors-and-Adjoint-Bispinors"><a class="docs-heading-anchor" href="#Bispinors-and-Adjoint-Bispinors">Bispinors and Adjoint Bispinors</a><a id="Bispinors-and-Adjoint-Bispinors-1"></a><a class="docs-heading-anchor-permalink" href="#Bispinors-and-Adjoint-Bispinors" title="Permalink"></a></h2><pre><code class="language-julia hljs">bs = rand(BiSpinor)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">4-element BiSpinor with indices SOneTo(4): | ||
0.059979213615885096 + 0.5654354586372555im | ||
0.6772399020689832 + 0.7084739862205124im | ||
0.7789630672622218 + 0.18455226328208896im | ||
0.07910382007786487 + 0.3375551411648158im</code></pre><pre><code class="language-julia hljs">abs = rand(AdjointBiSpinor)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">4-element AdjointBiSpinor with indices SOneTo(4): | ||
0.07224917236478556 + 0.9419672209712744im | ||
0.8211669156427549 + 0.9402496162141518im | ||
0.24086474620058473 + 0.9252560145785232im | ||
0.04883636719494855 + 0.13151640798213082im</code></pre><pre><code class="language-julia hljs">abs * bs</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">-0.6619678577458139 + 2.1079814674330017im</code></pre><h2 id="Dirac-and-Gamma-Matrices"><a class="docs-heading-anchor" href="#Dirac-and-Gamma-Matrices">Dirac and Gamma Matrices</a><a id="Dirac-and-Gamma-Matrices-1"></a><a class="docs-heading-anchor-permalink" href="#Dirac-and-Gamma-Matrices" title="Permalink"></a></h2><pre><code class="language-julia hljs">gm = rand(DiracMatrix)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">4×4 DiracMatrix with indices SOneTo(4)×SOneTo(4): | ||
0.749968+0.906041im 0.799362+0.357477im … 0.329876+0.430853im | ||
0.985028+0.117199im 0.330441+0.255369im 0.274491+0.104286im | ||
0.0605429+0.373808im 0.343195+0.0033193im 0.512458+0.11829im | ||
0.113548+0.787755im 0.709438+0.998444im 0.44538+0.845511im</code></pre><pre><code class="language-julia hljs">abs * gm * bs</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">-4.180775810583916 + 2.8005862643872352im</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../particles/">« Particles and Phase Space Points</a><a class="docs-footer-nextpage" href="../../library/outline/">Contents »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 11 November 2024 17:14">Monday 11 November 2024</span>. Using Julia version 1.10.6.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> |
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