Sample Quiz 9 Questions

True or False: Please provide brief justification
  * A real symmetric matrix is Hermitian.
  * A pure imaginary matrix that is anti-symmetric is Hermitian (i.e. all coefficients are imaginary).
  * If $H$ is an $n \times n$ Hermitian matrix, then $\overline{v^t}Hv$ is real.
  * If $A$ and $B$ are Hermitian, then so is their product $AB$.

More Questions
  * If $A$ is Hermitian, show that $iA$ is anti-Hermitian.
  * If $A$ is anti-Hermitian, show that $iA$ is Hermitian.
  * Find all matrices which are symmetric and anti-Hermitian.


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