## anonymous 4 years ago what is diagnolization in linear algebra?

1. TuringTest

I'm kind of weak in this area, so I'm just going to shoot you a link http://tutorial.math.lamar.edu/Classes/LinAlg/Diagonalization.aspx I'm sure somebody can explain it in their own words though... @UnkleRhaukus @nbouscal

2. anonymous

thanks

3. TuringTest

@Callisto @Chlorophyll how are you guys with linear algebra? wanna help?

4. anonymous

im totally lost. fml. my final is tomoro!!

5. anonymous

Why don't you ask a specific question? Your question is too general and it takes time to answer all aspects of it.

6. anonymous

okay: use the diagonlization theomr to find eignevalues of A and baisis for each eignespace: A= [ 2 -1 -1 1 4 1 -1 -1 2] =[ 1 -1 0 [ 3 0 0 [ 0 -1 -1 -1 1 -1 0 2 0 -1 -1 -1 0 -1 1] 0 0 3] -1 -1 0]

7. anonymous

i dont even understand what to do here!

8. anonymous

First find $Det( A - \lambda I)$

9. anonymous

of what? A?

10. anonymous

11. anonymous

bec the 3 matrix udner it is: PD(P-1)

12. anonymous

$Det(A-\lambda I)=-\lambda ^3+8 \lambda ^2-21 \lambda +18=(\lambda -3)^2 (2-\lambda )$ So it has 3 as a double eigenvalue and 2.

13. anonymous

$-\lambda^3+8\lambda^2-20\lambda+18$

14. anonymous

15. anonymous

dang it. how? isnt it 4 lambda 8 and 8 ?

16. anonymous

Now we have to find the eigenspace of 2 and the eigenspace of 3

17. anonymous

okay so how do we do it?

18. anonymous

A-3? A-2I?

19. anonymous

Find X such that AX = 2 X and Y such AY =3Y Y1={-1, 0, 1} Y2={-1, 1, 0} X={1, -1, 1} Y1, and Y2 is a basis for the eigenspace of 3 X is a basis for the eigensapce 2

20. anonymous

wooahhh. hold on. how did u do that? where are those y1 vextor from??

21. anonymous

I have to go to sleep now. Try to unersatnd how I got what I got. Bye.

22. anonymous

thnaks