Summary

This chapter brings the notions of span and linear independence together and talks about lists that are both linearly independent and span a vector space.

Important Definitions A basis of V is a list of vectors in V that is linearly independent and spans V.

Relevant Theorems

• 1753318207 - Axler 2.28 Criterion for basis
• 1753318207 - Axler 2.30 Every spanning list contains a basis
• 1753318233 - Axler 2.31 Every finite-dimensional vector space has a basis
• 1753318250 - Axler 2.32 Every linearly independent list extends to a basis
• 1753318265 - Axler 2.33 Every subspace of V is part of a direct sum equal to V