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what is diagnolization in linear algebra?

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

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Other answers:

im totally lost. fml. my final is tomoro!!
Why don't you ask a specific question? Your question is too general and it takes time to answer all aspects of it.
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]
i dont even understand what to do here!
First find \[Det( A - \lambda I) \]
of what? A?
A is your matrix.
bec the 3 matrix udner it is: PD(P-1)
\[ Det(A-\lambda I)=-\lambda ^3+8 \lambda ^2-21 \lambda +18=(\lambda -3)^2 (2-\lambda ) \] So it has 3 as a double eigenvalue and 2.
\[-\lambda^3+8\lambda^2-20\lambda+18\]
-21 instead of -20
dang it. how? isnt it 4 lambda 8 and 8 ?
Now we have to find the eigenspace of 2 and the eigenspace of 3
okay so how do we do it?
A-3? A-2I?
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
wooahhh. hold on. how did u do that? where are those y1 vextor from??
I have to go to sleep now. Try to unersatnd how I got what I got. Bye.
thnaks

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