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Vector Spaces

Algebraic structures formed by vectors that can be added and scaled.

Sequence of Expressions

Definition

A set

V

equipped with vector addition and scalar multiplication satisfying the 8 axioms.

Theorem

Beginner

For any linear map

f: V \to W

between finite-dimensional vector spaces,\n

\dim(V) = \text{rank}(f) + \text{nullity}(f)