1
Q
Theorem
Smith Normal Form
Proof
A
2
Q
Lemma
rank(T) is size of …
Proof
A
3
Q
Definition
Left and Right Linear Maps
A
4
Q
Definition
Row and Column Space and Rank
A
5
Q
Theorem
Elementary Transformations do not Affect Rank
Proof
A
6
Q
Corollary
Column Rank = Row Rank
Proof
A
7
Q
Theorem
Equivalences on A,B \in F^{m, n}
Proof
A
8
Q
Proposition
Canonical Form
A
9
Q
Lemma
Solving Systems and Gauss Method
A
10
Q
Definition
Row Echelon Form
A
11
Q
Definition
Row-reduced Echelon Form
A
12
Q
Theorem
Any Matrix can be Brought into Row-reduced Echelon Form
Proof
A
13
Q
Proposition
Existence of Solution to Systems
A
14
Q
Lemma
AB = I_{n}
Proof
A
15
Q
Lemma
(AB)^{-1} = B^{-1}A^{-1}
Proof
A
16
Q
Proposition
A
17
Q
Row-reduced Echelon Form of A is I_{n}
Proof
A
18
Q
Corollary
An Invertible Matrix is a Product of Elementary Transformations
Proof
A
