1. Vector Spaces Flashcards

1
Q

Definition
Vector Space

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Lemma
Properties of Vector Spaces

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Definition
Subspace

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Proposition
W1 \cap W2 is a Subspace
Proof

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Definition
W1 + W2

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Proposition
W1 + W2 is a Subspace
Proof

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Definition
Vector Sequence

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Definition
Linear Dependence

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Lemma
Test for Linear Dependence
Proof

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Proposition
Span is a Subspace
Proof

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Definition
Span

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Definition
Basis

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Proposition
Test for Basis
Proof

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Theorem
The Basis Theorem

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Definition
Dimension

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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