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By Kardi Teknomo, PhD.
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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 the product of matrices is independent of the order of their multiplication, that is
 . This can be extended into several matrices .
- 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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This tutorial is copyrighted.
Preferable reference for this tutorial is
Teknomo, Kardi (2011) Linear Algebra tutorial. http:\\people.revoledu.com\kardi\
tutorial\LinearAlgebra\ |
