--- a/main/linear-algebra/INDEX	Tue Oct 17 19:12:37 2006 +0000
+++ b/main/linear-algebra/INDEX	Tue Oct 17 22:18:07 2006 +0000
@@ -1,5 +1,6 @@
 matrix >> Linear Algebra
 Matrix functions
+ condeig
  funm
  thfm
 Matrix factorization

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main/linear-algebra/inst/condeig.m	Tue Oct 17 22:18:07 2006 +0000
@@ -0,0 +1,112 @@
+## Copyright (C) 2006 Arno Onken
+##
+## This program is free software; you can redistribute it and/or modify
+## it under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 2 of the License, or
+## (at your option) any later version.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; if not, write to the Free Software
+## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{c} =} condeig (@var{a})
+## @deftypefnx {Function File} {[@var{v}, @var{lambda}, @var{c}] =} condeig (@var{a})
+## Computes condition numbers for the eigenvalues of a matrix. The
+## condition numbers are the reciprocals of the cosines of the angles
+## between the left and right eigenvectors.
+##
+## Arguments are
+##
+## @itemize @bullet
+## @item
+## @var{a} must be a square numeric matrix.
+## @end itemize
+##
+## Return values are
+##
+## @itemize @bullet
+## @item
+## @var{c} is a vector of condition numbers for the eigenvalue of
+## @var{a}.
+##
+## @item
+## @var{v} is the matrix of right eigenvectors of @var{a}. The result is
+## the same as for @code{[v, lambda] = eig (a)}.
+##
+## @item
+## @var{lambda} is the diagonal matrix of eigenvalues of @var{a}. The
+## result is the same as for @code{[v, lambda] = eig (a)}.
+## @end itemize
+##
+## Example:
+##
+## @example
+## @group
+## a = [1, 2; 3, 4];
+## c = condeig (a)
+## @result{} [1.0150; 1.0150]
+## @end group
+## @end example
+## @end deftypefn
+
+## Author: Arno Onken <whyly@gmx.net>
+## Description: Condition numbers for eigenvalues
+
+function [v, lambda, c] = condeig (a)
+
+  # Check arguments
+  if (nargin != 1 || nargout > 3)
+    usage ("[v, lambda, c] = condeig (a)");
+  endif
+
+  if (! isempty (a) && ! ismatrix (a))
+    error ("condeig: a must be a numeric matrix");
+  endif
+
+  if (columns (a) != rows (a))
+    error ("condeig: a must be a square matrix");
+  endif
+
+  # Right eigenvectors
+  [v, lambda] = eig (a);
+
+  if (isempty (a))
+    c = lambda;
+  else
+    # Corresponding left eigenvectors
+    vl = inv (v)';
+    # Normalize vectors
+    vl = vl ./ repmat (sqrt (sum (abs (vl .^ 2))), rows (vl), 1);
+
+    # Condition numbers
+    # cos (angle) = (norm (v1) * norm (v2)) / dot (v1, v2)
+    # Norm of the eigenvectors is 1 => norm (v1) * norm (v2) = 1
+    c = abs (1 ./ dot (vl, v)');
+  endif
+
+  if (nargout == 0 || nargout == 1)
+    v = c;
+  endif
+
+endfunction
+
+%!test
+%! a = [1, 2; 3, 4];
+%! c = condeig (a);
+%! expected_c = [1.0150; 1.0150];
+%! assert (c, expected_c, 0.001);
+
+%!test
+%! a = [1, 3; 5, 8];
+%! [v, lambda, c] = condeig (a);
+%! [expected_v, expected_lambda] = eig (a);
+%! expected_c = [1.0182; 1.0182];
+%! assert (v, expected_v, 0.001);
+%! assert (lambda, expected_lambda, 0.001);
+%! assert (c, expected_c, 0.001);