spur

The trace of an n×n square matrix A is defined to be Tr(A) congruent sum_(i = 1)^n a_(i i), i.e., the sum of the diagonal elements. The matrix trace is implemented in the Wolfram Language as Tr[list]. In group theory, traces are known as "group characters." For square matrices A and B, it is true that Tr(A) | = | Tr(A^T) Tr(A + B) | = | Tr(A) + Tr(B) Tr(α A) | = | α Tr(A) (Lang 1987, p. 40), where A^T denotes the transpose.

group character | matrix | square matrix | tensor contraction | tensor trace