Question

3. Suppose A is symmetric positive definite and Q is an orthogonal matrix (square with orthonormal columns). True or false (with a reason or counterexample)?

a) (Q^(T))AQ is a diagonal matrix
b) (Q^(T))AQ is a symmetric positive definite matrix
c) (Q^(T))AQ has the same eigenvalues as A

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4. Compute (A^(T))A and A(A^(T)), and their eigenvalues, and eigenvectors of length one and calculate the singular value decomposition of the matrix:
[1 1 0]
A = [0 1 1]

any help would be appreciated, thanks!