matrix condition number is greater or equal to $1$

Theorem 1.

The matrix condition number is greater or equal $\mathrm{1}$.

Proof.

Let $A$ be a square matrix. Then by properties of a matrix norm,

$$1=||I||=||A{A}^{-1}||\le ||A^{-1}||||A||.$$

∎

Title	matrix condition number is greater or equal to $1$
Canonical name	MatrixConditionNumberIsGreaterOrEqualTo1
Date of creation	2013-03-22 15:28:15
Last modified on	2013-03-22 15:28:15
Owner	georgiosl (7242)
Last modified by	georgiosl (7242)
Numerical id	10
Author	georgiosl (7242)
Entry type	Theorem
Classification	msc 65F35
Classification	msc 15A12
Related topic	MatrixConditionNumber