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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `linear` mod in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, linear"><title>alga::linear - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc mod"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">☰</div><a href='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Module linear</p><div class="sidebar-elems"><div class="block items"><ul><li><a href="#traits">Traits</a></li></ul></div><p class='location'><a href='../index.html'>alga</a></p><script>window.sidebarCurrent = {name: 'linear', ty: 'mod', relpath: '../'};</script><script defer src="../sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>−</span>]</a></span><a class='srclink' href='../../src/alga/linear/mod.rs.html#1-16' title='goto source code'>[src]</a></span><span class='in-band'>Module <a href='../index.html'>alga</a>::<wbr><a class="mod" href=''>linear</a></span></h1><div class='docblock'><p>Traits dedicated to linear algebra.</p>
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</div><h2 id='traits' class='section-header'><a href="#traits">Traits</a></h2>
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<table><tr class='module-item'><td><a class="trait" href="trait.AffineSpace.html" title='alga::linear::AffineSpace trait'>AffineSpace</a></td><td class='docblock-short'><p>A set points associated with a vector space and a transitive and free additive group action
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(the translation).</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.AffineTransformation.html" title='alga::linear::AffineTransformation trait'>AffineTransformation</a></td><td class='docblock-short'><p>The group of affine transformations. They are decomposable into a rotation, a non-uniform
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scaling, a second rotation, and a translation (applied in that order).</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.DirectIsometry.html" title='alga::linear::DirectIsometry trait'>DirectIsometry</a></td><td class='docblock-short'><p>Subgroups of the orientation-preserving isometry group <code>SE(n)</code>, i.e., rotations and translations.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.EuclideanSpace.html" title='alga::linear::EuclideanSpace trait'>EuclideanSpace</a></td><td class='docblock-short'><p>The finite-dimensional affine space based on the field of reals.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.FiniteDimInnerSpace.html" title='alga::linear::FiniteDimInnerSpace trait'>FiniteDimInnerSpace</a></td><td class='docblock-short'><p>A finite-dimensional vector space equipped with an inner product that must coincide
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with the dot product.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.FiniteDimVectorSpace.html" title='alga::linear::FiniteDimVectorSpace trait'>FiniteDimVectorSpace</a></td><td class='docblock-short'><p>A finite-dimensional vector space.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.InnerSpace.html" title='alga::linear::InnerSpace trait'>InnerSpace</a></td><td class='docblock-short'><p>A vector space equipped with an inner product.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.InversibleSquareMatrix.html" title='alga::linear::InversibleSquareMatrix trait'>InversibleSquareMatrix</a></td><td class='docblock-short'><p>The group of inversible matrix. Commonly known as the General Linear group <code>GL(n)</code> by
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algebraists.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.Isometry.html" title='alga::linear::Isometry trait'>Isometry</a></td><td class='docblock-short'><p>Subgroups of the isometry group <code>E(n)</code>, i.e., rotations, reflexions, and translations.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.Matrix.html" title='alga::linear::Matrix trait'>Matrix</a></td><td class='docblock-short'><p>The space of all matrices.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.MatrixMut.html" title='alga::linear::MatrixMut trait'>MatrixMut</a></td><td class='docblock-short'><p>The space of all matrices that are stable under modifications of its components, rows and columns.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.NormedSpace.html" title='alga::linear::NormedSpace trait'>NormedSpace</a></td><td class='docblock-short'><p>A normed vector space.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.OrthogonalTransformation.html" title='alga::linear::OrthogonalTransformation trait'>OrthogonalTransformation</a></td><td class='docblock-short'><p>Subgroups of the n-dimensional rotations and scaling <code>O(n)</code>.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.ProjectiveTransformation.html" title='alga::linear::ProjectiveTransformation trait'>ProjectiveTransformation</a></td><td class='docblock-short'><p>The most general form of invertible transformations on an euclidean space.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.Rotation.html" title='alga::linear::Rotation trait'>Rotation</a></td><td class='docblock-short'><p>Subgroups of the n-dimensional rotation group <code>SO(n)</code>.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.Scaling.html" title='alga::linear::Scaling trait'>Scaling</a></td><td class='docblock-short'><p>Subgroups of the (signed) uniform scaling group.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.Similarity.html" title='alga::linear::Similarity trait'>Similarity</a></td><td class='docblock-short'><p>Subgroups of the similarity group <code>S(n)</code>, i.e., rotations, translations, and (signed) uniform scaling.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.SquareMatrix.html" title='alga::linear::SquareMatrix trait'>SquareMatrix</a></td><td class='docblock-short'><p>The monoid of all square matrices, including non-inversible ones.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.SquareMatrixMut.html" title='alga::linear::SquareMatrixMut trait'>SquareMatrixMut</a></td><td class='docblock-short'><p>The monoid of all mutable square matrices that are stable under modification of its diagonal.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.Transformation.html" title='alga::linear::Transformation trait'>Transformation</a></td><td class='docblock-short'><p>A general transformation acting on an euclidean space. It may not be inversible.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.Translation.html" title='alga::linear::Translation trait'>Translation</a></td><td class='docblock-short'><p>Subgroups of the n-dimensional translation group <code>T(n)</code>.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.VectorSpace.html" title='alga::linear::VectorSpace trait'>VectorSpace</a></td><td class='docblock-short'><p>A vector space has a module structure over a field instead of a ring.</p>
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