/en/tags/linear-algebra/Recent content in Linear-Algebra on Feynman's BlogHugoen-USTue, 21 Jul 2026 12:00:00 +0800/en/posts/games101-vectors-linear-algebra/Tue, 21 Jul 2026 12:00:00 +0800/en/posts/games101-vectors-linear-algebra/<blockquote class="blockquote-regular"> <p>Instructor: Lingqi Yan | UCSB Bilibili: <a href="https://www.bilibili.com/video/BV1X7411F744">https://www.bilibili.com/video/BV1X7411F744</a></p> </blockquote> <h2 id="1-vector-basics">1 Vector Basics</h2> <h3 id="definition-of-vectors">Definition of Vectors</h3> <p><img src="/images/2026-07-21_series_games101/02_vectors/chap2_01.png" alt="Vector Definition"></p> <ul> <li>Vectors have <strong>direction</strong> and <strong>length</strong>, but no absolute starting position</li> <li>Commonly denoted as $\vec{a}$ or bold <strong>a</strong></li> <li>Represented by start and end points: $\overrightarrow{AB} = B - A$</li> </ul> <h3 id="vector-normalization">Vector Normalization</h3> <ul> <li>Magnitude (length) of a vector: $||\vec{a}||$</li> <li><strong>Unit vector</strong>: A vector with magnitude 1, used to represent direction</li> <li>Normalization: $\hat{a} = \frac{\vec{a}}{||\vec{a}||}$</li> </ul> <h3 id="vector-addition">Vector Addition</h3> <ul> <li><strong>Geometric representation</strong>: Parallelogram law &amp; triangle law</li> <li><strong>Algebraic calculation</strong>: Add corresponding coordinates</li> </ul> $$ \vec{a} + \vec{b} = \begin{pmatrix} x_a + x_b \\ y_a + y_b \end{pmatrix} $$<p><strong>Geometric representation of vector addition</strong>:</p>