Layer 4 · Foundations

Linear Algebra

The formal definitions: vector spaces, norms, matrix rank, eigenvectors, and why they explain what a trained network 'keeps.'

15 min read180 XP

Dot product

similarity / projection

Norm

length of a vector

Rank

effective dimensionality

Eigenvector

direction unchanged by a transform

The four linear-algebra objects that recur throughout deep learning theory.

Formally, vectors live in a vector space $R^{d}$ closed under addition and scalar multiplication. The dot product defines both length and angle: