Lennie Carroll
2020-10-18
Answered

Define Hermitian Matrices.

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Khribechy

Answered 2020-10-19
Author has **100** answers

Step 1

Hermitian matrix is a complex square matrix that is equal to its own conjugate transpose, that is for which

$A={A}^{H}$

where${A}^{H}$ denotes the conjugate transpose.

In other words, we can say the matrix whose matrix whose element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column is called Hermitian matrix.

That is

${a}_{ij}={\overline{a}}_{ji}$

Step 2

For example, consider the matrix

$A=\left[\begin{array}{cc}1& -i\\ i& 1\end{array}\right]$

$\overline{A}=\left[\begin{array}{cc}1& i\\ -i& 1\end{array}\right]$

${\overline{A}}^{T}=\left[\begin{array}{cc}1& -i\\ i& 1\end{array}\right]$

${\overline{A}}^{T}=A$

Therefore, A is hermitian matrix.

Hermitian matrix is a complex square matrix that is equal to its own conjugate transpose, that is for which

where

In other words, we can say the matrix whose matrix whose element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column is called Hermitian matrix.

That is

Step 2

For example, consider the matrix

Therefore, A is hermitian matrix.

Jeffrey Jordon

Answered 2022-01-27
Author has **2027** answers

Answer is given below (on video)

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(b) Write it again as a product of ABC (same B) of three matrices.

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