## liliy Group Title what is diagnolization in linear algebra? 2 years ago 2 years ago

1. TuringTest Group Title

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. liliy Group Title

thanks

3. TuringTest Group Title

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

4. liliy Group Title

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

5. eliassaab Group Title

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

6. liliy Group Title

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. liliy Group Title

i dont even understand what to do here!

8. eliassaab Group Title

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

9. liliy Group Title

of what? A?

10. eliassaab Group Title

11. liliy Group Title

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

12. eliassaab Group Title

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

13. liliy Group Title

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

14. eliassaab Group Title

15. liliy Group Title

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

16. eliassaab Group Title

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

17. liliy Group Title

okay so how do we do it?

18. liliy Group Title

A-3? A-2I?

19. eliassaab Group Title

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. liliy Group Title

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

21. eliassaab Group Title

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

22. liliy Group Title

thnaks