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## Homework Statement

Suppose B is a real nonsingular matrix. Show that: (a) B

^{t}B is symmetric and (b) B

^{t}B is positive definite

2. Homework Equations

2. Homework Equations

N/A

## The Attempt at a Solution

I have managed to prove (a) by showing that elements that are symmetric on the diagonal are equal. However I have no idea how to prove B. I've tried to express [c

_{ij}] with sigma notation with no sucess. I've also tried to apply the rules of matrices to try and show that u

^{t}B

^{t}Bu is bigger than zero with no sucess as well (perhaps (Bu)

^{t}=uB?...). Any help would be greatly appriciated.