The Trace of Square Matrices and Properties of Trace

We define the trace of a square matrix to be the sum of the diagonal entries. While this quantity may seem as if it lacks power, its symmetry in the indices give it many invariant quantities which we discuss here. We prove that if trace(AB)=trace(BA), which plays an important role in the study of similarity of matrices. We also discuss how the trace of AA^T will help define the Frobenius norm of the matrix.

#mikethemathematician, #mikedabkowski, #profdabkowski