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MathGroup Archive 1996

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Re: Euclidean Matrix Norm

  • To: mathgroup at smc.vnet.net
  • Subject: [mg5340] Re: [mg5303] Euclidean Matrix Norm
  • From: Lou Talman <me at talmanl.mscd.edu>
  • Date: Wed, 27 Nov 1996 01:47:54 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

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  
symbolically.

--Lou Talman 


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