A square matrix A is said to be symmetric if its transpose AT satisfies AT= A,...

A square matrix A is said to be symmetric if its transpose A^T satisfies A^T= A, and a
complex-valued square matrix A is said to be Hermitian if its conjugate transpose A^H =
(A)^T = A^T satisfies A^H = A. Thus, a real-valued square matrix A is symmetric if and
only if it is Hermitian. Which of the following is a vector space?
(a) The set of all n xn real-valued symmetric matrices over R.
(b) The set of all n xn complex-valued symmetric matrices over C.
(c) The set of all nx n complex-valued Hermitian matrices over R.
(d) The set of all n xn complex-valued Hermitian matrices over C.
For each case, either verify that it is a vector space or prove otherwise.

Expert Solution

Colby Messinger answered 2 years ago

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