https://arshadhs.github.io/tags/convexity/Recent content in Convexity on Arshad SiddiquiHugoen-usThu, 29 Jan 2026 00:00:00 +0000https://arshadhs.github.io/docs/ai/maths/010-linear-algebra/01-linear-systems/convex/Thu, 29 Jan 2026 00:00:00 +0000https://arshadhs.github.io/docs/ai/maths/010-linear-algebra/01-linear-systems/convex/<h1 id="convex-combination-of-two-points"> Convex Combination of Two Points <a class="anchor" href="#convex-combination-of-two-points">#</a> </h1> <p>A <strong>convex combination</strong> describes how to form a point between two points using weighted averages.</p> <p>It is a fundamental building block in several advanced fields:</p> <ul> <li><strong>Linear Algebra &amp; Geometry</strong></li> <li><strong>Optimization Theory</strong></li> <li><strong>Machine Learning</strong> (Specifically in SVMs, clustering, and data interpolation)</li> </ul> <hr> <p>Given two points (or vectors) $\mathbf{x}_1, \mathbf{x}_2 \in \mathbb{R}^n$, a convex combination of these points is defined as:</p> $$\mathbf{x} = \lambda \mathbf{x}_1 + (1 - \lambda)\mathbf{x}_2$$<p><strong>Where:</strong></p>