# Diagonalisability problem and others

rainwyz0706

## Homework Statement

1.Prove that if A is a real matrix then At A is diagonalisable.

2. Given a known 3*3 matrix A, Calculate the maximum and minimum values of ||Ax|| on the sphere ||x|| = 1.

## The Attempt at a Solution

For the first problem, I'm thinking of proving that AtA is symmetric, but I'm not sure which properties to use.
For the second one, is X a 3*n matrix? Do I need to discuss n?
Any help is greatly appreciated!

Staff Emeritus
Homework Helper
If $B=A^TA$, write down what $B_{ij}$ and $B_{ji}$ are in terms of the elements of A and show that they're equal.