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MathGroup Archive 1996

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Re: Euclidean Matrix Norm

  • To: mathgroup at
  • Subject: [mg5351] Re: Euclidean Matrix Norm
  • From: Daniel Lichtblau <danl>
  • Date: Wed, 27 Nov 1996 01:48:04 -0500
  • Organization:
  • Sender: owner-wri-mathgroup at

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).
> Tanks,
> A.A.Gerritsen

The Euclidean norm is given by the largest singular value. You can get
this as
because (i) the list of singular values is the second component in the
output of SingularValues (the first and third being the pre- and
post-multiplier matrices; see usage message below), and (ii) the
singular values are ordered by decreasing magnitude.

In[12]:= ??SingularValues
SingularValues[m] gives the singular value decomposition for a numerical
   matrix m. The result is a list {u, w, v}, where w is the list of
   values, and m can be written as
Attributes[SingularValues] = {Protected}
Options[SingularValues] = {Tolerance -> Automatic}

Daniel Lichtblau
Wolfram Research
danl at

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