A Hermitian matrix is a square matrix with complex entries that is equal to its own conjugate.

True

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False

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Solution

The correct option is B
False

A Hermitian matrix is a square matrix with complex entries that is equal to its own conjugate Transpose.We know that if we take an element aij from a square matrix. The corresponding element in its transpose will be aji. If we take both transpose and conjugate the corresponding element becomes $¯ ¯¯¯¯¯ ¯ a j i$ . So by definition we can need, $¯ ¯¯¯¯¯ ¯ a j i = a i j$ for matrix to be Hermitian matrix.

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A Hermitian matrix is a square matrix with complex entries that is equal to its own conjugate.

A^{θ} = A

a_{i j} =_{j i}

A^{θ} = - A

a_{i j} = -_{j i}

A^{θ}

\to

f (A) = {\begin{matrix} 1 A i s h e r m i t i a n - 1 A i s s k e w h e r m i t i a n \end{matrix}

f (A - A^{θ}) =

If A is a square matrix then $A -^{T}$ is a skew hermitian matrix.

A^{θ} = A

a_{i j} =_{j i}

A^{θ} = - A

a_{i j} = -_{j i}

f : M \to {1, - 1}, M

f (A) = {\begin{matrix} 1 & A i s h e r m i t i a n - 1 & A i s s k e w h e r m i t i a n \end{matrix}

Y = A^{n}

A matrix with diagonal elements as complex numbers with imaginary part not 0 can never be Hermitian matrix

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