The Singular Value Decomposition (SVD) is a matrix factorization theorem stating that any real M×N matrix A with rank R can be uniquely decomposed into three matrices: U, Σ, and Vᵀ, where U and V are orthogonal square matrices representing rotations or reflections, and Σ is an M×N diagonal matrix containing non-negative singular values. In linear algebra, the core principle relies on eigenvalue decomposition of symmetric product matrices (Aᴬ and AᵗA) to derive scaling factors derived from eigenvectors that form orthonormal bases for the domain range, null space, and left null space, thereby enabling dimensionality reduction and signal processing applications.
The Singular Value Decomposition (SVD) is a matrix factorization theorem stating that any real M×N matrix A with rank R can be uniquely decomposed into three matrices: U, Σ, and Vᵀ, where U and V are…