trace
The trace $\mathrm{Tr}(A)$ of a square matrix^{} $A$ is defined to be the sum of the diagonal entries of $A$. It satisfies the following formulas:

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$\mathrm{Tr}(A+B)=\mathrm{Tr}(A)+\mathrm{Tr}(B)$

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$\mathrm{Tr}(AB)=\mathrm{Tr}(BA)$ ()
where $A$ and $B$ are square matrices of the same size.
The trace $\mathrm{Tr}(T)$ of a linear transformation $T:V\u27f6V$ from any finite dimensional vector space^{} $V$ 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 eigenvalues^{} of $T$ (over a splitting field^{} of the characteristic polynomial^{}), 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 functional^{} $\varphi :A\to \u2102$ that has the .
Title  trace 

Canonical name  Trace 
Date of creation  20130322 12:17:57 
Last modified on  20130322 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 