The trace Tr(A) of a square matrixMathworldPlanetmath A is defined to be the sum of the diagonal entries of A. It satisfies the following formulas:

  • Tr(A+B)=Tr(A)+Tr(B)

  • Tr(AB)=Tr(BA)  ()

where A and B are square matrices of the same size.

The trace Tr(T) of a linear transformation T:VV from any finite dimensional vector spaceMathworldPlanetmath V to itself is defined to be the trace of any matrix representation of T with respect to a basis of V. This scalar is independent of the choice of basis of V, and in fact is equal to the sum of the eigenvaluesMathworldPlanetmathPlanetmathPlanetmathPlanetmath of T (over a splitting fieldMathworldPlanetmath of the characteristic polynomialMathworldPlanetmathPlanetmath), including multiplicities.

The following link presents some examples for calculating the trace of a matrix.

A trace on a C*-algebra A is a positive linear functionalMathworldPlanetmath ϕ:A that has the .

Title trace
Canonical name Trace
Date of creation 2013-03-22 12:17:57
Last modified on 2013-03-22 12:17:57
Owner mhale (572)
Last modified by mhale (572)
Numerical id 10
Author mhale (572)
Entry type Definition
Classification msc 15A15
Classification msc 15A04
Related topic FrobeniusMatrixNorm