2. Linear Transformations Flashcards
1
Q
Definition
Linear Transformation
A
2
Q
Lemma
Properties of Linear Maps
Proof
A
3
Q
Proposition
Basis Admits Linear Maps
Proof
A
4
Q
Definition
Operations on Linear Maps
A
5
Q
Definition
Image and Kernel
A
6
Q
Proposition
Properties of Image and Kernel
Proof
A
7
Q
Theorem
dim(W1 + W2) = ?
A
8
Q
Definition
Complementary and Direct Sum
A
9
Q
Corollary
V = W1 (+) W2
A
10
Q
Definition
Rank and Nullity
A
11
Q
Theorem
The Dimension Theorem
Proof
A
12
Q
Corollary
T: U -> V and dim(U) = dim(V) then equivalences
Proof
A
.
13
Q
Definition
Singular Map
A
14
Q
Definition
Operations on Matrices (as Linear Maps)
A
15
Q
Proposition
Laws of Matrix Operations
A
