A square matrix A is said to be symmetric if its transposeAT satisfies AT= A, and a
complex-valued square matrix A is said to be Hermitian if itsconjugate transpose AH =
(A)T = AT satisfies AH = A. Thus,a real-valued square matrix A is symmetric if and
only if it is Hermitian. Which of the following is a vectorspace?
(a) The set of all n xn real-valued symmetric matrices overR.
(b) The set of all n xn complex-valued symmetric matrices overC.
(c) The set of all nx n complex-valued Hermitian matrices overR.
(d) The set of all n xn complex-valued Hermitian matrices overC.
For each case, either verify that it is a vector space or proveotherwise.
