Remarks on condition numbers and optimally conditioned matrices

• Main Authors: Estalilla, Aliento V., Pinpin, Lord Kenneth M.
• Format: text
• Published: Animo Repository 2005
• Subjects: Matrices—Norms; Numerical analysis; Hadamard matrices; Mathematics; Numerical Analysis and Computation
• Online Access: https://animorepository.dlsu.edu.ph/faculty_research/12784
• Institution: De La Salle University

Matrix condition numbers are proved to be submultiplicative but neither subadditive nor superadditive, and the Frobenius and the default (based on the 2-norm) condition numbers are shown to be unitarily invariant. The equality of all the singular values of a square matrix is established as a necessa...