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## Main Question or Discussion Point

Can a symmetric matrix contain complex elements(terms).

If no, how is it that 'eigen values of a symmetric matrix are always real'(from a theorem)

Is a symmetric matrix containing complex terms called a hermitian matrix or is there any difference?

Can we call the following matrix symmetric (A = transpose of A), even though its not hermitian. (A not equal to A dagger)

i i

i 2i

But its eigen values are not real contradicting the above theorem.

If no, how is it that 'eigen values of a symmetric matrix are always real'(from a theorem)

Is a symmetric matrix containing complex terms called a hermitian matrix or is there any difference?

Can we call the following matrix symmetric (A = transpose of A), even though its not hermitian. (A not equal to A dagger)

i i

i 2i

But its eigen values are not real contradicting the above theorem.