Hermitian and Skew  Hermitian Matrices
Hermitian Matrix:
A square matrix $A$ is Hermitian if it is equal to its conjugate transpose: $A={A}^{\u2020}$
 Properties:
 For a real matrix, being Hermitian is equivalent to being symmetric.
 For a complex matrix, the elements satisfy ${a}_{ij}=\stackrel{\u203e}{{a}_{ji}}$ for all $i$ and $j$.
 The diagonal elements must be real.
 Hermitian matrices are always square matrices.
Example of Hermitian Matrix:
In this case, $A={A}^{\u2020}$, which makes it a Hermitian matrix.
SkewHermitian Matrix:
A square matrix $A$ is skewHermitian if it is equal to the negative of its conjugate transpose: $A={A}^{\u2020}$
 Properties:
 For a real matrix, a skewHermitian matrix is equivalent to a skewsymmetric matrix.
 For a complex matrix, the elements satisfy ${a}_{ij}=\stackrel{\u203e}{{a}_{ji}}$ for all $i$ and $j$.
 The diagonal elements must be purely imaginary.
Example of SkewHermitian Matrix:
In this case, $A={A}^{\u2020}$, which makes it a skewHermitian matrix.
Properties of Hermitian and SkewHermitian Matrices:

Sum of Hermitian Matrices: The sum of two Hermitian matrices is also Hermitian. $A+B=C$ where $A$, $B$, and $C$ are Hermitian matrices.

Sum of SkewHermitian Matrices: The sum of two skewHermitian matrices is also skewHermitian. $A+B=C$ where $A$, $B$, and $C$ are skewHermitian matrices.

Product with Scalar: Both Hermitian and skewHermitian matrices preserve their property when multiplied by a scalar.