Determinant of non square matrix

In summary, the conversation discusses the topic of finding the determinant of non-square matrices. It is mentioned that the determinant is only defined for square matrices and that it represents the change in volume due to a change in basis vectors. A paper is suggested as a resource for finding the determinant of non-square matrices, but the person has difficulty understanding it. Another paper is mentioned, which offers a technique for finding the determinant of a 2x3 matrix. The conversation concludes with a request for any other techniques or resources for solving this problem.
  • #1
ahmednet24
5
0
how we can find the determinant of non square matrix ??
 
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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
  • #5
Download this paper and read first definition and first example and you see how they find the determinant of a matrix 2x3
 
  • #6
  • #7
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.
 
  • #8
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.
 
  • #9
ahmednet24 said:
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!)
 
  • #10
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
 

What is a determinant of a non square matrix?

A determinant is a mathematical value that can be calculated for a square matrix, which is a matrix with an equal number of rows and columns. However, it is also possible to calculate the determinant of a non square matrix, which is a matrix with a different number of rows and columns. The determinant of a non square matrix is used to determine the consistency and uniqueness of a system of linear equations.

How do you calculate the determinant of a non square matrix?

The determinant of a non square matrix can be calculated by first creating a square matrix from the non square matrix by adding rows or columns of zeros. Then, the determinant can be calculated using the same methods as a square matrix, such as Gaussian elimination or Cramer's rule.

What does the determinant of a non square matrix represent?

The determinant of a non square matrix represents the signed volume of the parallelepiped spanned by the columns or rows of the matrix. In other words, it represents the scaling factor of the transformation described by the matrix.

Why is the determinant of a non square matrix important?

The determinant of a non square matrix is important because it is used to determine the consistency and uniqueness of a system of linear equations. It can also be used to calculate the inverse of a non square matrix, which is useful in solving systems of equations and in various applications in physics and engineering.

Can the determinant of a non square matrix be negative?

Yes, the determinant of a non square matrix can be negative. The sign of the determinant depends on the number of row and column swaps required to put the matrix into its reduced row echelon form. If an odd number of swaps is required, the determinant will be negative, and if an even number of swaps is required, the determinant will be positive.

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