Question

Two Linear Algebra exercises

Answer 1

Let be \[A,B \in K^{n x n}\] such that A.B=B.A and let \[E_{\lambda} = \left\{x \in K^{n} / A.x = \lambda . x \right\}\]
Prove that \[E_\] is invariant

Answer 2

\[E_{\lambda}\] *

Answer 3

Lets be \[A,B \in K^{n x n}\] two diagonalizables matrix such that A.B = B.A
Prove that there's \[C \in GL(n,K)\] which \[C.A.C^{-1}\] and \[C.B.C^{-1}\] are diagonals. (With the same C).

Answer 4

K is a generic field.

Answer 5

I guess I'll have to keep trying xD

Answer 6

you should try Linear algebra by david c lay 4th edition..chapter 5 eigen values and eigen vectors..i can give you if you want

Answer 7

I already read some theory, but reading more never hurts, so feel free to give me it to me :D

Answer 8

lol ok wait