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