Trace of a square matrix is the summation of matrix diagonal entries . Trace of a matrix is also called spur of a square matrix.
: Given matrix
The diagonal matrix is
Thus, the trace is
Some important properties of the trace of a matrix are
- Trace of a matrix is a linear operation. Trace of a summation or subtraction of two matrices is equal to the summation or subtraction of trace of the matrices, that is
- Trace of a matrix transpose is equal to the trace of the original matrix