X is a matrix with dimension M X N.

a) Is H = XX^HSymmetric? Hermetian?

b) Is G = X^HX Symmetric? Hermetian?

c) Calculate the order of the number of floating point multiplications that are needed to compute G and H. Are these orders the same? If they are, justify why they are the same. If not, which one is more onerous to compute G or H? Justify.

d) If you can, compute the trace of G and the trace of H. If you can compute both, what is the relation between them.

e) If you can compute the trace of G and the trace of H, calculate the order of the number of floating point multiplications that are needed to compute each trace. Are these orders the same? If they are, justify why they are the same. If not, which one is more onerous to compute, the trace of G or the trace of H? Justify.