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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Disciplines

Mathematics | Numerical Analysis and Computation

Keywords

Matrices—Norms; Numerical analysis; Hadamard matrices

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