Matrix Eigenvalues and UFO Pyramids: A Geometric Journey from Theory to Structure
1. Foundations: Matrix Eigenvalues and Orthogonal Transformations Eigenvalues and eigenvectors define how linear transformations stretch or rotate space. In finite-dimensional vector spaces, an eigenvector \( \mathbf{v} \) of a square matrix \( A \) satisfies \( A\mathbf{v} = \lambda \mathbf{v} \), where \( \lambda \) is the eigenvalue—the scaling factor along \( \mathbf{v} \). Orthogonal […]
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