what is diagnolization in linear algebra?

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what is diagnolization in linear algebra?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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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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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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