# matrix condition number is greater or equal to $1$

###### Theorem 1.

The matrix condition number is greater or equal $1$.

###### Proof.

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

 $1=||\,I\,||=||\,AA^{-1}\,||\leq||\,A^{-1}\,||||\,A\,||.$

Title matrix condition number is greater or equal to $1$ MatrixConditionNumberIsGreaterOrEqualTo1 2013-03-22 15:28:15 2013-03-22 15:28:15 georgiosl (7242) georgiosl (7242) 10 georgiosl (7242) Theorem msc 65F35 msc 15A12 MatrixConditionNumber