I am reading the book, "Linear Algebra and Learning from Data", 2019 edition. Section 1.9, subsection, "The Linear Algebra behind PCA", has the following line - "Principal Component Analysis is a way to understand n sample points $a_1, ..., a_n$ in m-dimensional space -the data"
Subsequently Equation 21 is used to compute the total variance of the data -
$T = (||a_1||^2+...+||a_n||^2)/(n-1)$
I don't understand this equation. It seems like the author is computing the variance across samples. As per my understanding, variance should be computed across features. I'd highly appreciate some clarification over this.