1
Q
Definition
Vector Space
A
2
Q
Lemma
Properties of Vector Spaces
A
3
Q
Definition
Subspace
A
4
Q
Proposition
W1 \cap W2 is a Subspace
Proof
A
5
Q
Definition
W1 + W2
A
6
Q
Proposition
W1 + W2 is a Subspace
Proof
A
7
Q
Definition
Vector Sequence
A
8
Q
Definition
Linear Dependence
A
9
Q
Lemma
Test for Linear Dependence
Proof
A
10
Q
Proposition
Span is a Subspace
Proof
A
11
Q
Definition
Span
A
12
Q
Definition
Basis
A
13
Q
Proposition
Test for Basis
Proof
A
14
Q
Theorem
The Basis Theorem
A
15
Q
Definition
Dimension
A
16
Q
Lemma
Sifting
Proof
A
17
Q
Proposition
Linearly Independent Sequence <= dim(V)
Proof
A
18
Q
Theorem
Subsequence of Span is Basis
Proof
A
19
Q
Corollary
Span Admits a Basis
A
20
Q
Corollary
Any Span of Length dim(V) is a Basis
Proof
A
21
Q
Theorem
Basis Extension
Proof
A
22
Q
Corollary
Linearly Independent Sequence of Length dim(V) is a Basis
A
