Determinant of a non-square matrix?
in [Matlab]
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From: Joerg Buchholz on 1 Jul 2010 06:47 "John D'Errico" <woodchips(a)rochester.rr.com> wrote in message <i0hnk0$6nv$1(a)fred.mathworks.com>... > "Joerg Buchholz" <buchholz(a)hs-bremen.de> wrote in message <i0h9lp$3t6$1(a)fred.mathworks.com>... > > Is there a determinant of a non-square matrix? > > > > >> det ([sym('a'), sym('b')]) > > > > ans = > > > > a > > No. Determinant has no mathematical definition for a > non-square matrix, at least not traditionally so. > > There is one attempt to make such a definition, already > found on the file exchange. I recall that I strongly > disagreed with dett when the file was submitted, but > it does still exist on the FEX. > > Why do you wish to use such a tool? If your goal is > simply to identify if the matrix is singular, then a > determinant is ALWAYS the WRONG thing to use!!!! > Any such determinant here will have numerical > problems, and will not reliably predict the singularity > status of your matrix in floating point arithmetic. > Instead use rank, a far more reliable tool, that already > is found in every matlab installation. If rank returns > a number that is less than min(size(A)) for a given > matrix A, then A is numerically singular, and this is a > reliable test. > > John John, I second every word you say! But - Matlab computes the determinant of a symbolic non-square matrix without the slightest warning (see my example). I just wanted to make sure that there is not a mathematically agreed definition of a non-square determinant before I file a bug report. Joerg
From: Faraz Afzal on 1 Jul 2010 07:18 "Jan Simon" <matlab.THIS_YEAR(a)nMINUSsimon.de> wrote in message <i0hqr4$sdb$1(a)fred.mathworks.com>... > 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 Hey Jan .. I m sending you email but it is popping back. DNS requested is not being recognized.. I already attached the paper and sent it to Joerg. If you have a direct access try this www.emis.de/journals/BAG/vol.46/no.2/b46h2rad.pdf Regards, Muhammad Faraz
From: Jan Simon on 1 Jul 2010 07:45 Dear Faraz, > I m sending you email but it is popping back. DNS requested is not being recognized.. There are some obviously more or less obvious changes in my email address. > www.emis.de/journals/BAG/vol.46/no.2/b46h2rad.pdf Thanks! And the name of the article is "About a determinant of rectangular $2\times n$ matrix and its geometric interpretation", Mirko Radi'c Jan
From: Joerg Buchholz on 1 Jul 2010 08:34 Mirko Radic defined a determinant of a rectangular matrix in 1966: http://www.zentralblatt-math.org/zmath/scans.html?volume_=168&count_=027 Nevertheless, Matlab does not use Mirko's definition to compute symbolic rectangular matrices. Matlab seems to returns the determinant of the left mxm submatrix of an mxn matrix if m<n: >> a = [a11 a12 a13; a21 a22 a23] a = [ a11, a12, a13] [ a21, a22, a23] >> det (a) ans = a11*a22 - a12*a21 If m>n, Matlab throws an error: >> a = [a11 a12; a21 a22; a31 a32] a = [ a11, a12] [ a21, a22] [ a31, a32] >> det (a) ??? Error using ==> mupadmex Error in MuPAD command: second index out of range [(Dom::Matrix(Dom::ExpressionField()))::_index] Error in ==> sym.sym>sym.det at 1437 d = mupadmex('mllib::det',A.s);
From: Faraz Afzal on 1 Jul 2010 08:56
"Joerg Buchholz" <buchholz(a)hs-bremen.de> wrote in message <i0i1vs$p0m$1(a)fred.mathworks.com>... > Mirko Radic defined a determinant of a rectangular matrix in 1966: > > http://www.zentralblatt-math.org/zmath/scans.html?volume_=168&count_=027 > > Nevertheless, Matlab does not use Mirko's definition to compute symbolic rectangular matrices. Matlab seems to returns the determinant of the left mxm submatrix of an mxn matrix if m<n: > > >> a = [a11 a12 a13; a21 a22 a23] > > a = > > [ a11, a12, a13] > [ a21, a22, a23] > > >> det (a) > > ans = > > a11*a22 - a12*a21 > > If m>n, Matlab throws an error: > > >> a = [a11 a12; a21 a22; a31 a32] > > a = > > [ a11, a12] > [ a21, a22] > [ a31, a32] > > >> det (a) > ??? Error using ==> mupadmex > Error in MuPAD command: second index out of range [(Dom::Matrix(Dom::ExpressionField()))::_index] > > Error in ==> sym.sym>sym.det at 1437 > d = mupadmex('mllib::det',A.s); Thats true.. All the information is true. But what my concern is if the information i have given helped u solving ur problem.. Let Matlab do tehre own procedures but as long as ur problem is concerned if u got 2xn matrix that page would be enough to solve ur problem.. Let me know if i helped you in any ways.. Regards, Muhammad Faraz |