8. Eigenvalues and Eigenvectors Flashcards
1
Q
Definition
Eigenvector and Eigenvalue I
A
2
Q
Definition
Eigenvector and Eigenvalue II
A
3
Q
Theorem
Root of Characteristic Polynomial
Proof
A
4
Q
Theorem
Diagonalisable Matrix
Proof
A
5
Q
Proposition
Eigenvalues of Triangular Matrix
Proof
A
.
6
Q
Theorem
Eigenvectors are Linearly Independent
Proof
A
7
Q
Corollary
Distinct Eigenvalues => Diagonalisable
Proof
A
8
Q
Corollary
A, B Similar <=> Same Eigenvalues
A
9
Q
Theorem
A^{2} = Tr(A) A - det(A) I_{2}
Proof
A
10
Q
Corollary
A Similar to B = (?)
Proof
A
11
Q
Lemma
Canonical Repeated Real
A
12
Q
Lemma
Canonical Distinct Real
A
13
Q
Lemma
Canonical Complex
A
