# Determinant using Laplace expansion

• combosco
In summary, the Laplace expansion method is a technique used to find the determinant of a square matrix by breaking it down into smaller determinants. It can be used for any square matrix, but is most commonly used for larger ones. The formula for finding the determinant using this method involves expanding along a row or column and adding the products of elements and their cofactors. However, there are limitations to using this method, such as its applicability only to square matrices and its increasing complexity with larger matrices. For non-square matrices, other methods must be used to find the determinant.
combosco
Hello!
Do somebody know where the code for calculating a determinant by Laplace theorem (in Fortran) can be found? Or maybe somebody could help with this issue.
Thank you!

## 1. What is the Laplace expansion method for finding determinants?

The Laplace expansion method is a technique used to find the determinant of a square matrix. It involves expanding the determinant along a row or column and breaking it down into smaller determinants, until the final value is found.

## 2. When should the Laplace expansion method be used?

The Laplace expansion method is useful for finding the determinant of any square matrix, regardless of its size. However, it is most commonly used for larger matrices as it can be time-consuming for smaller ones.

## 3. What is the formula for finding the determinant using Laplace expansion?

The formula for finding the determinant using Laplace expansion is:
det(A) = a11C11 + a12C12 + ... + a1nC1n
Where aij is the element in the first row and jth column, and Cij is the cofactor of that element.

## 4. Are there any limitations to using Laplace expansion for finding determinants?

Yes, there are some limitations to using Laplace expansion for finding determinants. This method can only be used for square matrices, and it becomes increasingly complex as the size of the matrix increases. Additionally, it may not be the most efficient method for finding determinants of larger matrices.

## 5. Can the Laplace expansion method be used for non-square matrices?

No, the Laplace expansion method can only be used for square matrices. For non-square matrices, other methods such as Gaussian elimination or finding the eigenvalues may be used to find the determinant.

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