Remarks on condition numbers and optimally conditioned matrices

• المؤلفون الرئيسيون: Estalilla, Aliento V., Pinpin, Lord Kenneth M.
• التنسيق: text
• منشور في: Animo Repository 2005
• الموضوعات: Matrices—Norms; Numerical analysis; Hadamard matrices; Mathematics; Numerical Analysis and Computation
• الوصول للمادة أونلاين: https://animorepository.dlsu.edu.ph/faculty_research/12784
• المؤسسة: 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 necessary and sufficient condition for the matrix to be optimally conditioned under the 2-norm, making unitary, Hadamard and some diagonal and antidiagonal matrices possess unity condition numbers.