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