# Homework Help: Proving a Theorem, related to Gerschgorin

1. Sep 21, 2011

### syj

1. The problem statement, all variables and given/known data
Here is the theorem I need to prove:

For A=(aij)$\in$Cnxn

we have

p(A)$\leq$$max_{i}$$\Sigma^{n}_{j=1}$|aij|

2. Relevant equations

3. The attempt at a solution

2. Sep 21, 2011

### CompuChip

Some definitions might be nice.
What is $C_{n \times n}$? What is $p(A)$? What does i run over?

3. Sep 21, 2011

### syj

Sorry,
Cnxn is the set of nxn matrices with entries in the complex number system.

p(A)= max{|$\lambda$1|, |$\lambda$2|, ...}

p(A) is the smallest circle in the comple plane, centered at the origin, which contains all the characteristic values of A.

4. Sep 21, 2011

### CompuChip

Maybe it's a good idea to start with the simple case, where A is diagonalizable.