Determinant of a non-square matrix?
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From: Joerg Buchholz on 1 Jul 2010 01:39 Is there a determinant of a non-square matrix? >> det ([sym('a'), sym('b')]) ans = a
From: Jan Simon on 1 Jul 2010 05:15 Dear Joerg, > Is there a determinant of a non-square matrix? > >> det ([sym('a'), sym('b')]) > ans = > a How do you define "determinant of a non-square matrix" ? As far as I know and after asking wikipedia I have the impression, that "determinant" are defined for square matrices only. Jan
From: John D'Errico on 1 Jul 2010 05:37 "Joerg Buchholz" <buchholz(a)hs-bremen.de> wrote in message <i0h9lp$3t6$1(a)fred.mathworks.com>... > Is there a determinant of a non-square matrix? > > >> det ([sym('a'), sym('b')]) > > ans = > > a No. Determinant has no mathematical definition for a non-square matrix, at least not traditionally so. There is one attempt to make such a definition, already found on the file exchange. I recall that I strongly disagreed with dett when the file was submitted, but it does still exist on the FEX. Why do you wish to use such a tool? If your goal is simply to identify if the matrix is singular, then a determinant is ALWAYS the WRONG thing to use!!!! Any such determinant here will have numerical problems, and will not reliably predict the singularity status of your matrix in floating point arithmetic. Instead use rank, a far more reliable tool, that already is found in every matlab installation. If rank returns a number that is less than min(size(A)) for a given matrix A, then A is numerically singular, and this is a reliable test. John
From: Faraz Afzal on 1 Jul 2010 05:49 "Jan Simon" <matlab.THIS_YEAR(a)nMINUSsimon.de> wrote in message <i0hmb8$h3l$1(a)fred.mathworks.com>... > Dear Joerg, > > > Is there a determinant of a non-square matrix? > > >> det ([sym('a'), sym('b')]) > > ans = > > a > > How do you define "determinant of a non-square matrix" ? > As far as I know and after asking wikipedia I have the impression, that "determinant" are defined for square matrices only. > > Jan Dears, If you have a 2xn Rectangular matrix then you can find its determinant for sure. I dont know if MATLAB can do this for you or not. But there is no problem them algorithm is simple enough to write in MATLAB .. For reference look through this paper appeared in EMIS (The European Mathematical Information Service) Journal. Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Volume 46 (2005), No. 1, 321-349. May be you have a matrix in 2xn form then you have your problem solved. Let me know if it helped. Regards, Muhammad Faraz
From: Jan Simon on 1 Jul 2010 06:32
Dear Faraz, > If you have a 2xn Rectangular matrix then you can find its determinant for sure. How? > I dont know if MATLAB can do this for you or not. But there is no problem them algorithm is simple enough to write in MATLAB .. For reference look through this paper appeared in EMIS (The European Mathematical Information Service) Journal. > Beiträge zur Algebra und Geometrie > Contributions to Algebra and Geometry > Volume 46 (2005), No. 1, 321-349. Could you post the name of the article, please? Looking in the online service, I cannot find anything after the page 300: http://www.emis.de/journals/BAG/vol.46/no.1/17.html Jan |