Normal Matrices Examples ( )

  • Thread starter tazzzdo
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  • #1
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Normal Matrices Examples (URGENT)

I need to produce 2 x 2 normal matrices A and B such that A + B is not normal. I have proven that AB is normal if AB = BA using the Householder matrix form. But I can't find a form for A + B failing to be normal.

A matrix A with entries a, b, c, d is going to be normal if b = c. But that means a matrix B has to have b = c to be normal as well. So A + B will have 2b, 2c for the 1,2 and 2,1 entries as well which will make A + B normal.

Unless I'm totally off. I have to get this done in the next 3 hours.
 

Answers and Replies

  • #2
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Please don't write things like

I have to get this done in the next 3 hours.

or "urgent". You will actually get less replies that way.
 
  • #3
berkeman
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Schoolwork?
 
  • #4
mathwonk
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relax, the world will not end if this drags out.

I suggest starting by thinking up a really simple non normal matrix, then try to realize it as A+B where A and B are a little nicer. (This took me about 30 seconds.)
 
  • #6
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I don't understand how to make a non-normal matrix break down into 2 normal matrices. That's the whole point of my post.
 
  • #7
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I don't understand how to make a non-normal matrix break down into 2 normal matrices. That's the whole point of my post.

Can you give us an example of a non-normal matrix?
 
  • #8
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1 1
0 1

There is no way to make that matrix the sum of 2 normal matrices A and B?
 
Last edited:
  • #9
Dick
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1 1
0 1

There is no way to make that matrix the sum of 2 normal matrices A and B?

Sure there's a way. Try and write it as the sum of a symmetric matrix and an antisymmetric matrix.
 
Last edited:
  • #10
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Now I understand. I used

0 1
1 0

and

0 -1
1 0
 
  • #11
Dick
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Now I understand. I used

0 1
1 0

and

0 -1
1 0

Sure. That works.
 
  • #12
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Love being in grad school and missing stupid things like that. -__- Preciate the help.
 
  • #13
mathwonk
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nice hint, micro mass. good job, tazzzdo.
 

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