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## #1 2014-04-01 17:44:15

iLloyd054
Member
Registered: 2014-04-01
Posts: 10

### Matrix

(a)                    2,1,0
Is matrix  0,2,0    diagonalisable?
0,0,2

(b)                       3,-2,3
A is a matrix   1,2,1
1,3,0

(i)    Find the  eigenvalues.

(ii)    Find P-1 and B such that P-1AP = B where B is a diagonal matrix

Last edited by iLloyd054 (2014-04-01 17:58:41)

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## #2 2014-04-01 19:37:11

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Matrix

Hi iLloyd054;

a) It should be because it has three distinct eigenvalues. See c) for the actual diagonalization.

b) The eigenvalues of that matrix are 4, 2, -1.

c)

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #3 2014-04-01 23:03:42

iLloyd054
Member
Registered: 2014-04-01
Posts: 10

### Re: Matrix

thank you so much bobbym I appriciate that...

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## #4 2014-04-01 23:21:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Matrix

Hi;

You are welcome and  welcome to the forum.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #5 2014-04-02 12:49:41

eigenguy
Member
Registered: 2014-03-18
Posts: 78

### Re: Matrix

(A) No. Perhaps bobbym sees something distinct about each of those 2s, but they all look the same to me. That matrix is already in Jordan normal form, and that superdiagonal 1 tells me that the eigenspace of 2 is going to be 2 dimensional (if there were a second superdiagonal 1, it would only be one dimensional).

"Having thus refreshed ourselves in the oasis of a proof, we now turn again into the desert of definitions." - Bröcker & Jänich

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## #6 2014-04-02 13:45:10

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Matrix

No nothing different I was referring to the matrix in part b which was not the question asked in a).

a) is not diagonalizable.

Sorry for the confusion.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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