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SVT

Singular Value Decomposition (SVD)
  • a mathematical technique used in linear algebra to factorize a matrix into three other matrices
    • Given a matrix A of size m×n, SVD expresses it as: \(A=UΣV^{T}\)
    • U \(\rightarrow\) An m*m orthogonal matrix whose columns are the left singular vectors of A
    • Σ \(\rightarrow\) An m×n diagonal matrix with non-negative real numbers on the diagonal, known as the singular values of A. These values are ordered from largest to smallest.
    • \(V^{T}\) \(\rightarrow\) transpose of an n×n orthogonal matrix whose columns are the right singular vectors of A.
  • SVD is a powerful tool for data analysis and dimensionality reduction across various fields, including statistics, machine learning, and computer vision.\