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Finite Vector Space

Explore the concept of finite vector spaces defined over finite fields, learning how to verify vector space axioms such as closure, commutativity, and associativity. Understand how these properties apply to vectors and operations through practical Python code examples, strengthening your grasp of vector space fundamentals in data science.

Definition

A vector space that has a finite number of elements is known as a finite vector space. Such a vector space is defined over a finite field.

Example

Consider a finite field F={0,1}F=\{0,1\} with an ++ operator that’s overloaded as (a+b)mod2(a+b)\mod 2. Also consider V={[00],[01],[10],[11]}V=\bigg\{ \begin{bmatrix}0\\0 ...