Answer to Question #467 in Matrix | Tensor Analysis for Patrick Nwenne

Question

Prove that the trace of a matrix A i.e TR(A)=sum of the diagonal elements of A.

Answer 1

The trace of an square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A. Equivalently, the trace of a matrix is the sum of its eigenvalues, making it an invariant with respect to a change of basis. This characterization can be used to define the trace for a linear operator in general. Note that the trace is only defined for a square matrix (i.e. n×n).