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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 303

Diagonalizing, and its related problem of finding eigenvalues and eigenvectors, is a major subject of research for Numerical mathematics. For 5 dimensions or higher, it can only be done by iterative methods.

And what is wrong with iterative methods? Do you know that you can diagonalize an 8 by 8 when it is possible even with floating point numbers? [comment removed]

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

Stefy wrote:

bob bundy wrote:

the incident matrix has exactly two ones and 6 zeros in each column.

Why is that?

If I have understood this correctly an incidence matrix has n rows for the n vertices, and m columns for the lines.

Thus, if a line, L1, joins points 1 and 2, the incidence matrix will have a 1 in position (1,1) and another 1 in position (1,2). The rest of the first column will have zeros. As every line has two endpoints (you won't let me have loops) then every column has two 1s and the rest of the column has zeros.

So I is such a matrix. And I'm using A to represent the adjacency matrix. If point x is adjacent to point y, then point y is adjacent to point x; hence A is symmetric.

If that definition of similar is the one to use, then we want

for some invertible matrix P.

I thought this:

My 'hot favourite' solution turns out to be an I with no inverse, , so back to the drawing board.

Maybe the OP has more information that would help, such as a few theorems leading up to this question.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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*Last edited by Agnishom (2014-04-14 02:17:31)*

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

hi Agnishom,

That about sums it up. Mom didn't mumble anything about graph theory did she?

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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But she talked about eigenvectors.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

**Online**