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Re: [mg5303] Euclidean Matrix Norm
Posted:
Nov 26, 1996 3:41 AM


Armin Gerritsen wrote:
> Does anyone know if Mathematica (2.2.2) can calculate the Euclidean > matrixnorm of a matrix. (== max Ax/A , where x a nonzero 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



