6. The Determinant Flashcards
1
Q
Definition
The Determinant
A
2
Q
Definition
Characteristic Polynomial
A
3
Q
Definition
Types of Matrix
A
4
Q
Proposition
Determinant of Triangular Matrix
Proof
A
.
5
Q
Theorem
Elementary Transformations on Determinant
A
6
Q
Definition
Cofactor and Adjoint Matrix
A
7
Q
Theorem
A adj(A) = ?
A
8
Q
Corollary
det(A) != 0 => ?
A
9
Q
Theorem
det(A^{T}) = det(A)
A
10
Q
Lemma
det(EB) = det(E)det(B)
Proof
A
11
Q
Theorem
det(A) = 0 <=> A Singular
Proof
A
12
Q
Theorem
det(AB) = det(A)det(B)
Proof
A
13
Q
Corollary
det(A^{-1}) = det(A)^{-1} when?
Proof
A
14
Q
Corollary
A orthogonal then det(A) = ?
Proof
A
15
Q
Corollary
If A, B similar? Proof
A
