## anonymous 3 years ago Two Linear Algebra exercises

1. anonymous

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

2. anonymous

$E_{\lambda}$ *

3. anonymous

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).

4. anonymous

K is a generic field.

5. anonymous

I guess I'll have to keep trying xD

6. anonymous

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

7. anonymous

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

8. anonymous

lol ok wait