2. Linear Systems Flashcards
1
Q
Lemma 2.2 (Matrix Exponential)
and definition.
Proof.
A
2
Q
Lemma 2.3
e^{At} is… and ….
Proof.
A
3
Q
Corollary 2.4
Solution to linear system IVP.
Proof.
A
4
Q
Lemma 2.5
e^{P^{-1}AP} = …
Proof.
A
5
Q
Lemma 2.7
If AB = BA then…
Proof.
A
6
Q
Corollary 2.8
e^{-A} = …
Proof.
A
7
Q
Theorem 2.9 (Jordan Normal Form for 2x2 Matrices)
A
8
Q
Theorem 2.10 (Instability)
Proof.
A
9
Q
Proposition 2.16
Let A = diag{A_1, …, A_m}, then ||A|| = …
Proof?
A
10
Q
Corollary 2.17
Suppose A has Jordan normal form J = diag{J_1, …, J_k}, then…
Proof.
A
11
Q
Theorem 2.18 (Stability I)
Proof.
A
12
Q
Theorem 2.19 (Stability II)
Proof.
A
13
Q
Remark 2.20
Deducing eigenvalue signs from trace and det.
A
14
Q
Phase portrait: node.
A
15
Q
Phase portrait: saddle point.
A
16
Q
Phase portrait: star.
A
17
Q
Phase portrait: improper node.
A
18
Q
Phase portrait: centre and foci.
A
