Note
Let U be a subspace of
and let B be a finite subset of U we say that B is a basis for U if
- B is linearly independent
- U = Span B
Standard Basis- Letbe the columns of the n x n identity matrix I. The set { } is a basis for , called the standard basis for - Standard basis for
is { } = { , }
- Standard basis for
- If B =
is a basis for , then k = n, that is, every basis for consists of exactly n vectors - Let B = {
} be a set of n vectors in . Then B spans if and only if B is linearly independent