https://www.chenk.top/en/tags/eigenvectors/Recent content in Eigenvectors on Chen Kai BlogHugoenWed, 05 Feb 2025 09:00:00 +0000https://www.chenk.top/en/linear-algebra/06-eigenvalues-and-eigenvectors/Wed, 05 Feb 2025 09:00:00 +0000https://www.chenk.top/en/linear-algebra/06-eigenvalues-and-eigenvectors/<p><figure class="article-figure"> <img src="https://blog-pic-ck.oss-cn-beijing.aliyuncs.com/posts/en/linear-algebra/06-eigenvalues-and-eigenvectors/illustration_1.png" alt="Essence of Linear Algebra (6): Eigenvalues and Eigenvectors — Chapter overview" loading="lazy" decoding="async" class="content-image"> </figure> </p> <hr> <h2 id="the-big-question" class="heading-anchor">The Big Question<a href="#the-big-question" class="heading-link" aria-label="Permalink to this section" title="Copy link to this section">#</a> </h2><p>Apply a matrix to a vector and almost anything can happen. Most vectors get rotated <em>and</em> stretched, landing in a brand new direction. But scattered among them are a few special vectors that refuse to leave their span. They come out of the transformation pointing exactly the way they went in — only longer, shorter, or flipped.</p>