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The Little Book of Linear Algebra
There is hardly any theory which is more elementary than linear algebra, in spite of the fact that generations of professors and textbook writers have obscured its simplicity by preposterous calcul...
Matrix multiplication is the core mechanism of linear algebra: it encodes how transformations combine, how systems of equations are solved, and how data flows in modern algorithms. Orthonormal bases simplify every aspect of linear algebra: solving systems, computing projections, expanding functions, diagonalizing symmetric matrices, and working with Fourier series. At its core, PCA is an application of the spectral theorem to covariance matrices: it finds orthogonal directions (principal components) that capture the maximum variance in data.
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