Notice that the first and last ones are always the trace and determinant.

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Nov 29, 2022 · In this paper, I present some properties of the trace function, which operates on square matrices. A basic knowledge matrices is assumed, and, in particular, that of the determinant of a matrix.

3.1 Properties of Matrix Trace In this part we record the properties of the trace that we ta. ked about in. and B 2 Rk n, Tr(AB) = Tr(BA): The matrix dot product is de ned analo. ous to the vector dot pro. asy …

These slides are provided for the NE 112 Linear algebra for nanotechnology engineering course taught at the University of Waterloo. The material in it reflects the authors’ best judgment in light of the …

This document is a more in-depth discussion of trace, which I hinted at in class. Some of it requires material from later in the course, so you can refer back to this when they are introduced.

Now, define the trace of a matrix as the sum of its diagonal entries. Then, for matrices A and B, trace(A + B) = trace A + trace B straight from the definition of matrix addition.