Year: 2017
Type: preprint
Abstract: It is well known the concept of the condition number $κ(A) = \|A\|\|A^{-1}\|$, where $A$ is a $n \times n$ real or complex matrix and the norm used is the spectral norm. Although it is very common to think in $κ(A)$ as "the" condition number of $A$, the truth is that condition numbers are associated to problems, not just instance of problems. Our goal is to clarify this difference. We will introduce the general concept of condition number and apply it to the particular case of real or complex matrices. After this, we will introduce the classic condition number $κ(A)$ of a matrix and show some known results.
Source: arXiv (Cornell University)
Author: Diniz, Felipe Bottega
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2595874093