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Topic: Re: [mg5303] Euclidean Matrix Norm
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Lou Talman

Posts: 876
Registered: 12/3/04
Re: [mg5303] Euclidean Matrix Norm
Posted: Nov 26, 1996 3:41 AM
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Armin Gerritsen wrote:

> Does anyone know if Mathematica (2.2.2) can calculate the Euclidean
> matrix-norm of a matrix. (== max |Ax|/|A| , where x a non-zero vector and A
> a square matrix).

The matrix norm of the square matrix A is the square root of the largest
eigenvalue of the matrix (Transpose[A] . A), so put

Norm[A_] := Sqrt[Max[N[Eigenvalues[Transpose[A].A]]]]

Of course, this gives only a numeric approximation. Life is more difficult if
you want the norm symbolically, because Mathematica can't find the Max

--Lou Talman

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