Skew-Hermitian Matrix
A complex square matrix is said to be a skew-Hermitian matrix if the conjugate transpose matrix is equal to the negative of the original matrix. A square matrix “An×n = [aij] is said to be a Hermitian matrix if AH = -A, where AH is the conjugate transpose of matrix A.
- Matrix given below is a Hermitian matrix of order “2 × 2.”
Now, the conjugate of A ⇒
The conjugate transpose of matrix A ⇒
We can see that AH = −A, so the given matrix is a skew-Hermitian matrix.
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Hermitian Matrix
A rectangular array of numbers that are arranged in rows and columns is known as a “matrix.” The size of a matrix can be determined by the number of rows and columns in it. If a matrix has “m” rows and “n” columns, then it is said to be an “m by n” matrix and is written as an “m × n” matrix. For example, a matrix with five rows and three columns is a “5 × 3” matrix. We have various types of matrices, like rectangular, square, triangular, symmetric, singular, etc. Now let us discuss the Hermitian matrix in detail.