SVD Formulas & Reference

Linear Algebra for Machine Learning · Axiom Academy

Complete Reference for Singular Value Decomposition U is m × m orthogonal matrix (left singular vectors) Σ is m × n diagonal matrix (singular values) V T is n × n orthogonal matrix (right singular vectors) Keep only the first k singular values: Truncated SVD: k(m + n + 1) elements For singular or non-square matrices: where Σ + contains reciprocals of non-zero singular values A applies transformation as: first rotate (V T ), then scale (Σ), then rotate (U)

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