Say, I have a matrix M of shape n x d. M'M results in a square matrix of shape d x d. How can I interpret M'M?
import numpy as np
M = np.array([[1, 2], [2, 1], [3, 4], [4, 3]])
prod = M.T.dot(M)
2026-03-31 12:14:24.1774959264
How to interpret the square matrix M'M?
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Think of your matrix as $d$ vectors in $n$ dimensions. The product matrix is the matrix of dot products of your vectors, and so describes completely the geometry of the simplex spanned by these vectors.