Lecture Notes

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.