What is the best book to learn probability theory through a linear algebra perspective? I have heard from my linear algebra professor in undergraduate studies that probability theory can be examined using linear algebra.
As a math student who enjoys linear algebra, does anyone have a good textbook that uses linear algebra to examine probability theory?

One book that explores probability from a linear algebraic point of view is Hilbert Space Methods in Probability and Statistical Inference by Christopher G. Small and Don L. McLeish. From the introduction:

In the traditional approach to probability and statistics, the
starting point is the concept of the sample space and a class of
subsets called events. The Hilbert space approach shifts the starting
point away from the sample space and replaces it with a Hilbert space
whose elements can be variously interpreted as random variables,
estimating functions, or other quantities depending on the data and
the parameter.

But be aware that this book is almost 30 years old (published 1994), and I don't know to what extent practicing probabilists or mathematical statisticians work within this framework today. (Also note that basic linear and matrix algebra is the natural language for multivariate probability and statistics. The Hilbert space view here is more general.)
