trace

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

•
$\\operatorname{Tr}(A+B)=\\operatorname{Tr}(A)+\\operatorname{Tr}(B)$
•
$\\operatorname{Tr}(AB)=\\operatorname{Tr}(BA)$ ()

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

The trace $\\operatorname{Tr}(T)$ of a linear transformation $T\\colon V\\longrightarrow V$ 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 $\\phi\\colon A\\to\\mathbb{C}$ that has the .

单词	Trace
释义	trace The trace $\\operatorname{Tr}(A)$ of a square matrix $A$ is defined to be the sum of the diagonal entries of $A$ . It satisfies the following formulas: • $\\operatorname{Tr}(A+B)=\\operatorname{Tr}(A)+\\operatorname{Tr}(B)$ • $\\operatorname{Tr}(AB)=\\operatorname{Tr}(BA)$ () where $A$ and $B$ are square matrices of the same size. The trace $\\operatorname{Tr}(T)$ of a linear transformation $T\\colon V\\longrightarrow V$ 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 $\\phi\\colon A\\to\\mathbb{C}$ that has the .
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