This chapter discusses the notion of dimension of a finite dimensional vector space. It defines dimension and shows that no matter the basis, the dimension stays the same ie the length of the list of basis vectors is the same no matter which basis you pick.
Important Definitions The dimension of a finite dimensional vector space is the length of any basis of the vector space. It is denoted by dim V.
Relevant Theorems * 1753403565 - Axler 2.34 Basis length does not depend on basis * 1753403591 - Axler 2.37 Dimension of a subspace * 1753403620 - Axler 2.38 Linearly independent list of the right length is a basis * 1753403670 - Axler 2.39 Subspace of full dimension equals whole sapce * 1753403714 - Axler 2.42 Spanning list of the right length is a basis * 1753403742 - Axler 2.43 Dimension of a sum