Any square matrix can be uniquely expressed as the sum of a symmetric and skew-symmetric matrix.
Proof
Let
be a square matrix. Then Then
Thus
is symmetric. And Thus,
is skew-symmetric.
Created: May 30, 2023Last Modified: Mar 14, 2024
Any square matrix can be uniquely expressed as the sum of a symmetric and skew-symmetric matrix.
Proof
Let
be a square matrix. Then Then
Thus
is symmetric. And Thus,
is skew-symmetric.