## matrix 2-norm?

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rolo91
Posts: 38
Joined: Mon Aug 06, 2012 10:21 am UTC

### matrix 2-norm?

I'm doing some school work, related to a matlab course, and I'm having some problems regarding the 2-norm of a matrix.

I don't understand it quite well, because my results won't fit what's expected.

Im supossed to find the 2-condition of a Wilson matrix, which apparently is equal to

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`|||a||| * |||a^-1|||`

where |||a||| is the 2-norm of the matrix a.

Now, according to my notes the 2-norm of a matrix a is equal to the square root of its largest eigenvalue (in absolute terms). so, my code goes something like this:

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`norm = sqrt(max(eig(A)))invnorm= sqrt(max(abs(eig(inv(A)))))result = norm*invnorm`

however, when I use the matlab command cond to check the solution, the result is totally different ( my code gives a number around 50 and matlab gives me a number around 3000).

What am I doing wrong? Are my definitions of norm and condition number correct?

Xenomortis
Not actually a special flower.
Posts: 1447
Joined: Thu Oct 11, 2012 8:47 am UTC

### Re: matrix 2-norm?

I confess to not being entirely certain what it is you're doing, but I think you've got the norm wrong.
|A|2 = sqrt( max{|eigenvalues of A*A|})
i.e., the 2-norm of A is the squareroot of the largest eigenvalue of A*A

(A* being the conjugate transpose of A)

(Late Edit: I meant 2-norm, not determinant squared; the statement was correct, but the notation confusing)
Last edited by Xenomortis on Fri Nov 16, 2012 4:54 pm UTC, edited 1 time in total. rolo91
Posts: 38
Joined: Mon Aug 06, 2012 10:21 am UTC

### Re: matrix 2-norm?

You are completely right!

That was my problem, I had a wrong definition of 2-norm in my notes. Using your definition, it works flawlessly.

Thanks!