Matrix Condition Number Estimation

CONDITION is a FORTRAN90 library which implements methods for computing or estimating the condition number of a matrix.

Let ||*|| be a matrix norm, let A be an invertible matrix, and inv(A) the inverse of A. The condition number of A with respect to the norm ||*|| is defined to be

        kappa(A) = ||A|| * ||inv(A)||

If A is not invertible, the condition number is taken to be infinity.

Facts about the condition number include:

The CONDITION library needs access to a copy of the R8LIB library.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


CONDITION is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

LINPACK_D, a FORTRAN90 library which solves linear systems using double precision real arithmetic;

NAPACK, a FORTRAN77 library which includes many routines for applied numerical linear algebra tasks, including the matrix condition number, by William Hager.

R8LIB, a FORTRAN90 library which contains many utility routines using double precision real (R8) arithmetic.

TEST_MAT, a FORTRAN90 library which defines test matrices for which some of the determinant, eigenvalues, inverse, null vectors, P*L*U factorization or linear system solution are already known.


  1. Alan Cline, Cleve Moler, Pete Stewart, James Wilkinson,
    An estimate for the Condition Number of a Matrix,
    Technical Report TM-310,
    Argonne National Laboratory, 1977.
  2. Alan Cline, Russell Rew,
    A set of counterexamples to three condition number estimators,
    SIAM Journal on Scientific and Statistical Computing,
    Volume 4, Number 4, December 1983, pages 602-611.
  3. William Hager,
    Condition Estimates,
    SIAM Journal on Scientific and Statistical Computing,
    Volume 5, Number 2, June 1984, pages 311-316.
  4. Nicholas Higham,
    A survey of condition number estimation for triangular matrices,
    SIAM Review,
    Volume 9, Number 4, December 1987, pages 575-596.
  5. Diane OLeary,
    Estimating matrix condition numbers,
    SIAM Journal on Scientific and Statistical Computing,
    Volume 1, Number 2, June 1980, pages 205-209.
  6. Pete Stewart,
    Efficient Generation of Random Orthogonal Matrices With an Application to Condition Estimators,
    SIAM Journal on Numerical Analysis,
    Volume 17, Number 3, June 1980, pages 403-409.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN90 source codes.

Last revised on 05 October 2012.