Matrix Trace
Trace of a
square matrix
is the summation of matrix diagonal entries
. Trace of a matrix is also called
spur
of a square matrix.
Example
: Given matrix
The
diagonal matrix
is
Thus, the trace is
The interactive program below produces trace of your matrix input. The input matrix is shown back for your feedback. Random Example button will generate random square matrix at random order.
Properties
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
See also : matrix diagonal , matrix multiplication , matrix transpose
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