Introducing the matrix trace

The trace is a quantity that only applies to square matrices, such as the covariance matrix often encountered in ML. It is denoted as tr(A) for a square matrix, A, and is calculated as the sum of the diagonal elements in a square matrix. Let’s take a look:

1. In the following code snippet, we are creating a 3x3 matrix, A, and using the diag() function to extract the diagonal elements and sum them up to obtain the trace of the matrix. Note that we first create a DataFrame consisting of three columns, each having three elements, and then convert it into a matrix format to store in A:

   A = as.matrix(data.frame("c1"=c(1,2,3),"c2"=c(2,5,2),"c3"=c(-1,8,3)))
   >>> A
        c1 c2 c3
   [1,]  1  2 -1
   [2,]  2  5  8
   [3,]  3  2  3
   >>> diag(A)
   [1] 1 5 3
   >>> sum(diag(A))
   [1] 9

2. Since there is no built-in...