Vector Space

Learn the definition of vector space and its axioms and see examples.

Definition

A vector space, VV, defined over a field, FF, is a set with addition (++) and scalar multiplication (×\times) operations, obeying the following axioms.

Note: For the axioms below, consider x,y,z,0,xˉV\bold{x,y,z,0,\bar{x}}\in V and α,β,1F\alpha,\beta,1 \in F.

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