Determinant of non square matrix

[ahmednet24]

how we can find the determinant of non square matrix ??

 

[phyzguy]

The determinant is only defined for square matrices. You can think of the determinant as the change in the volume element due to a change in basis vectors. So if the number of basis elements is not the same (i.e. the matrix isn't square), then the determinant really doesn't make any sense.

 

[ahmednet24]

we can find the determinant of non square matrix but I don't have resource only this paper
(GENERALIZATION OF SOME DETERMINANTAL IDENTITIES FOR NON-SQUARE MATRICES BASED ON RADIC’S DEFINITION) But I have problem to understand it you can find this paper on google.

 

[HallsofIvy]

I haven't seen that paper but the title you give does not say anything about a non-square matrix having a determinant. It sounds like it is looking at analogues of identities that apply to determinants of square matrices.

 

[ahmednet24]

Download this paper and read first definition and first example and you see how they find the determinant of a matrix 2x3

 

[AlephZero]

You gave a link to a paper that answers your original question - so what is your question?

Google suggests there is some use for this in image processing. Here's a paper by the guy who "invented" the idea: http://www.emis.de/journals/BAG/vol.46/no.2/b46h2rad.pdf

 

[ahmednet24]

in fact I try to understand the paper that I mention to it,I don't know how they find the determinant of a matrix of size 2x3, My problem I have to find the determinant of a matrix 3x15.

 

[Norwegian]

To find your 3x15 generalized determinant, you need to compute the determinant of all the 455 3x3 submatrices, and take the alternating sum. The sign of the first determinant is positive, then the signs alternate according to the parity of the sum of the colomn indices.

 

[AlephZero]

in fact I try to understand the paper that I mention to it,I don't know how they find the determinant of a matrix of size 2x3

It was written out as the sum of three 2x2 determinants somewhere in the paper. (I'm not going back to find the exact page number for you!)

 

[ahmednet24]

I am thankful to all of you who try to help other, please if anyone have a paper or any other Technique to solve the problem who to find the determinant of non square matrix please share it with us