Remarks on condition numbers and optimally conditioned matrices
College
Gokongwei College of Engineering
Department/Unit
Manufacturing Engineering and Management
Document Type
Conference Proceeding
Source Title
Second Humanoid, Nanotechnology, Information Technology, Communication and Control, Environment, and Management (HNICEM) International Coference
Publication Date
3-2005
Abstract
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.
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Recommended Citation
Estalilla, A. V., & Pinpin, L. M. (2005). Remarks on condition numbers and optimally conditioned matrices. Second Humanoid, Nanotechnology, Information Technology, Communication and Control, Environment, and Management (HNICEM) International Coference Retrieved from https://animorepository.dlsu.edu.ph/faculty_research/12784
Disciplines
Mathematics | Numerical Analysis and Computation
Keywords
Matrices—Norms; Numerical analysis; Hadamard matrices
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