https://catinashell.de/tags/linalg/ Recent content in Linalg on Cat in a Shell Hugo en-us Fri, 10 Jul 2026 19:48:53 +0200 https://catinashell.de/math/singular-value-decomposition/ Fri, 10 Jul 2026 12:43:37 +0200 https://catinashell.de/math/singular-value-decomposition/ <p>Singular Value Decomposition allows factorisising an arbitrary matrix (real or complex), while a lot of other matrix factorization like with diagonalising etc. has often contraints.</p> <span class="katex"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>A</mi><mo>=</mo><mi>U</mi><mi mathvariant="normal">Σ</mi><msup><mi>V</mi><mi>T</mi></msup></mrow><annotation encoding="application/x-tex"> A = U \Sigma V^T </annotation></semantics></math></span><style> .heading { text-decoration: none; } .heading:hover { color: rgba(200,200,255,0.7); } .heading-anchor { margin-left: -1em; position: absolute; opacity: 0; text-decoration: none; transition: opacity 0.15s; } h1:hover .heading-anchor, h2:hover .heading-anchor, h3:hover .heading-anchor, h4:hover .heading-anchor, h5:hover .heading-anchor, h6:hover .heading-anchor { opacity: 1; } </style> <a href="#manually" class="heading"> <h3 id="manually"> <div class="heading-anchor" aria-label="Link to this section"> # </div> Manually </h3> </a> <p>I&rsquo;m showing this in an example, making it more visually appealing and understandable than some formal way (which I&rsquo;m also quite bad at writing xD)</p>