Matrix inverse

1. Jun 29, 2005

flop

Given that $C$ is a matrix and that $I - C$ is invertible, could someone show me the following?

$\|(I - C)^{-1}\| \leq \|I\| + \|C\| + \|C\|^2 + \cdots$

2. Jun 29, 2005

Hurkyl

Staff Emeritus
That formula looks awfully similar to:

$$\frac{1}{1 - x} = 1 + x + x^2 + x^3 + \cdots$$

Maybe the method of proof is similar?

3. Jun 29, 2005

flop

got it! thank you hurky