Question
Show that a real Hermitian matrix is symmetric. Show that a real unitary matrix is orthogonal.
Step 1
By definition, a Hermitian matrix is one that is equal to its own conjugate transpose. So, we have $A = A^*$, where $A^*$ denotes the conjugate transpose of $A$. Show more…
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Key Concepts
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Show that a real Hermitian matrix is symmetric. Show that a real unitary matrix is orthogonal. Note: Thus we see that Hermitian is the complex analogue of symmetric, and unitary is the complex analogue of orthogonal. (See Section 11.)
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