Decomposition into Symmetric and Skew-Symmetric Matrices

Decomposition into Symmetric and Skew-Symmetric Matrices

## Formula

Any square matrix $$a$$ can be written as:

$$A=\frac{A+A^T}{2}+\frac{A-A^T}{2}$$

where:

$$\frac{A+A^T}{2}$$

is symmetric and:

$$\frac{A-A^T}{2}$$

is skew-symmetric.

## Usage

- Used to express any square matrix as the sum of a symmetric and a skew-symmetric matrix.