The 1-norm is the largest column sum and the infinity norm the largest row sum; for example, see
??http://mathworld.wolfram.com/MatrixNorm.html
??http://en.wikipedia.org/wiki/Matrix_norm
The column sums of matrix([a,b,c]) are |a|, |b|, and |c|. So
?(%i54) mat_norm(matrix([a,b,c]),1);
?(%o54) max(abs(a),abs(b),abs(c))
The row sum of matrix([a,b,c]) is |a| + |b| + |c|. So
?(%i55) mat_norm(matrix([a,b,c]),inf);
?(%o55) abs(c)+abs(b)+abs(a)
--Barton
-----maxima-bounces at math.utexas.edu wrote: -----
To: maxima <maxima at math.utexas.edu>
From: Kostas Oikonomou <ko at research.att.com>
Sent by: maxima-bounces at math.utexas.edu
Date: 09/16/2010 02:14PM
Subject: matrix norm (mat_norm) problem?
Hi,
It seems to me that the definitions of the 1-norm and the
infinity-norm are switched in maxima 5.22.1:
(%i1) m : matrix([a,b,c]);
(%o1) ? ? ? ? ? ? ? ? ? ? ? ? ? ? [ a ?b ?c ]
(%i2) [mat_norm(m,inf), mat_norm(m,1)];
(%o2) ? ? ? [abs(c) + abs(b) + abs(a), max(abs(a), abs(b),
abs(c))]
(%i3)
???????? ???????? ???????? ???????? Kostas
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