Matrix properties
Having defined the eigenvectors and eigenvalues of a matrix, we can now introduce some additional matrix properties that can be useful later. Specifically, we will introduce the trace and determinant of a square matrix. These two quantities quantify some useful aspects of a matrix. Since we are simply giving their definitions here, this will be a relatively short section.
Trace
The trace of a square 
matrix 
is simply the sum of its diagonal elements. If has matrix elements 
, then the trace of 
is calculated as follows:
Eq. 54
Note the abbreviated notation, 
, that is commonly used when denoting the trace of a matrix. Now it turns out that the trace of a square matrix is also equal to the sum of its eigenvalues (we state this without proof), so that for a square matrix , which has eigenvalues 
, we can calculate its trace using the following formula:
Eq. 55
Often, when working with data science algorithms involving square matrices, we need...
