Re: Re: Euclidean Matrix Norm

• To: mathgroup at smc.vnet.net
• Subject: [mg5366] Re: [mg5340] Re: [mg5303] Euclidean Matrix Norm
• From: Allan Hayes <hay at haystack>
• Date: Thu, 5 Dec 1996 14:50:13 -0500
• Sender: owner-wri-mathgroup at wolfram.com

Lou Talman <me at talmanl.mscd.edu>
>Subject: [mg5340] Re: [mg5303] Euclidean Matrix Norm

>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]]]]

Lou,
Better move the N inside:

A = Table[Random[Integer,{-9,9}],{4},{4}]
{{-9, -9, 9, -1}, {-7, -6, -4, 1}, {-3, 0, 1, -4}, {3, 2, -5, 2}}

Sqrt[Max[N[Eigenvalues[Transpose[A].A]]]]//Timing
-15
List::nord: Comparison with complex number 0.0174327 - 2.55892 10    I
-15
{1.35 Second, Sqrt[Max[{0.0174327 - 2.55892 10    I,
-15                        -16
19.8739 + 3.16651 10    I, 77.0539 - 6.37398 10    I,
-17
317.055 + 2.98003 10    I}]]}

Chop[%]

But with N inside

Sqrt[Max[Eigenvalues[Transpose[A//N].A//N]]]//Timing
Allan Hayes
hay at haystack.demon.co.uk
http://wwe.haystack.demon.co.uk

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