Symmetric and Skew Symmetric Matrices A symmetric matrix is a square matrix that is equal to its transpose. This means that the elements in the matrix a...
Symmetric and Skew Symmetric Matrices
A symmetric matrix is a square matrix that is equal to its transpose. This means that the elements in the matrix are the same in the upper and lower triangular parts.
For example:
is a symmetric matrix.
A skew symmetric matrix is a square matrix that is not symmetric, but whose transpose is symmetric. This means that the elements in the matrix are the same in the upper and lower triangular parts, but they are not the same in the diagonal.
For example:
is a skew symmetric matrix.
The trace of a matrix is the sum of the elements in the diagonal. The trace of a symmetric matrix is equal to the trace of its transpose. The trace of a skew symmetric matrix is not equal to the trace of its transpose.
Symmetric and skew symmetric matrices have a number of important properties, including:
A symmetric matrix is symmetric.
A skew symmetric matrix is skew symmetric.
The trace of a symmetric matrix is equal to the trace of its transpose.
The trace of a skew symmetric matrix is not equal to the trace of its transpose