In: Advanced Math
A square matrix A is said to be symmetric if its transpose
AT satisfies AT= A, and a
complex-valued square matrix A is said to be Hermitian if its
conjugate 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 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.