[scilab-Users] Problem with Floating point and determinant of a matrix

[Manjusha Joshi]

Hello,

>
>
>
> -->det(A)
>  ans  =
>
>     6.661D-16  <---------- it should be 0
>
> -->inv(A)
>  ans  =
>
>  10^15 *
>
>   - 4.5035996    9.0071993  - 4.5035996
>     9.0071993  - 18.014399    9.0071993
>   - 4.5035996    9.0071993  - 4.5035996            <---------- it should
> appear
> an error message because the matrix A is not invertible (or singular).
>
>
> -->det(inv(A))
>  ans  =
>
>     9.007D+15     <-------------- The determinant of invertible
> matrix A^(-1)
> does not exist.
>
> Other example:
>
> -->B = [1 1; 1 1]
> B  =
>
>     1.    1.
>     1.    1.
>
> -->det(B)
>  ans  =
>
>     0.  <-------- it is correct !!
>
> -->inv(B)
>        !--error 19    <-------- it is correct !!
>
>
> The previously examples show two integer matrices A and B. The determinant
> of
> matrix A is quite zero, but not,
> and this can propagate an error in case the Scilab developer uses that
> result
> into other future calculations or algorithms.
> The determinant of matrix B is equal to 0 and the answer is correct. In
> case the
> Scilab developer uses that value,
> he or she can use the simple statement for testing like to:
>  if ( det(matrix) <> 0 ) then
> <action 1>                     // The Scilab developer knows that the
> matrix is
> invertible (or nonsingular)
> else
> <action 2>                     // The Scilab developer knows that the
> matrix is
> not invertible (or singular)
> end
>
> My doubt: "How can I proceed to design any algorithm, which uses matrix, if
> the
> determinant of
>
> the matrix could not be zero and, as the same time, that matrix is not
> invertible ?".
> How can I manage this uncertainty ?
>
>
clean(det(A))
clean(inv(B))

This will return value  as zero if it is near to zero.
-- 
Manjusha S. Joshi
P.I. of project on Use of Open source software for Teaching Maths,
 http://fossme.bprim.org
Lecturer in Computational  Mathematics,
BIM, Pune, India. www.bprim.org
Mobile:  09822 319328
blog:http://manjushajoshi.wordpress.com/
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