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mcyoung.xyz | ||
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lisyarus.github.io
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thenumb.at
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| | | | | [AI summary] The text discusses the representation of functions as vectors and their applications in various domains such as signal processing, geometry, and physics. It explains how functions can be treated as vectors in a vector space, leading to the concept of eigenfunctions and eigenvalues, which are crucial for understanding and manipulating signals and geometries. The text also covers different types of Laplacians, including the standard Laplacian, higher-dimensional Laplacians, and the Laplace-Beltrami operator, and their applications in fields like image compression, computer graphics, and quantum mechanics. The discussion includes spherical harmonics, which are used in representing functions on spheres, and their applications in game engines and glo... | |
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hadrienj.github.io
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| | | | | In this post, we will see special kinds of matrix and vectors the diagonal and symmetric matrices, the unit vector and the concept of orthogonality. | |
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austinmorlan.com
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| | | It took me longer than necessary to understand how a rotation transform matrix rotates a vector through three-dimensional space. Not because it's a difficult concept but because it is often poorly explained in textbooks. Even the most explanatory book might derive the matrix for a rotation around one axis (e.g., x) but then present the other two matrices without showing their derivation. I'll explain my own understanding of their derivation in hopes that it will enlighten others that didn't catch on right away. | ||
