Understand The Trace of a Matrix for Beginners – Deep Learning Tutorial

The trace of a matrix is a basic operation in deep learning, in this tutorial, we will descripe the basic definition and some facts on it, you can learn how to use it in your ai application.

What is the matrix trace?

As a square matrix A(n*n) = [a_ij], the trace of matrix A is defined:

For example:

The facts about matrix trace

Suppose k, k₁, …,  k_m ∈R and A, A₁, …, A_m are each n*n matrices.

Meanwhile.

However, one of the most important feature of matrix trace is on matrix eigenvalues and eigenvectors.

For example:

If matrix A is n*n.

Ax = λx

where x is eigenvector of A and λ is eigenvalues of A.

then