Every real m×n matrix factors as A = UΣV^T with U, V orthogonal and Σ diagonal of non-negative singular values σ_k. Yields rank, condition number σ_1/σ_r, low-rank best-approximant (Eckart-Young), pseudo-inverse, and the Frobenius identity…
Every real m×n matrix factors as A = UΣV^T with U, V orthogonal and Σ diagonal of non-negative singular values σ_k. Yields rank, condition number σ_1/σ_r, low-rank best-approximant (Eckart-Young), pseudo-inverse, and the Frobenius identity…