# Determinant of a non square matrix

• praharmitra
In summary, the conversation is discussing the concept of a determinant for non-square matrices. There is a question about whether there is a definition for this type of determinant, and the response is that it may not have the same properties as the determinant for square matrices. The conversation suggests that it is possible to define a "determinant-like" concept for non-square matrices, but it may be a challenging task to make it useful and intuitive.
praharmitra
Is there a definition of determinant of a non - square matrix??

What would you like that determinant "to do"?
Many of the roles played by the ordinary determinant for square matrices simply won't be inherited by your type of determinant. And what would then be the point of specifying an algorithm that would have as its output some number we call the "determinant" of that matrix?

I'm sure you could define a 'determinant like' thing for non-square matrices. Just define it however you need it and make it match intuition.

You would want to make sure that it had useful properties and obeyed regular properties of determinants. It could be quite an undertaking to come up with anything useful.

## What is a determinant of a non square matrix?

The determinant of a non square matrix is a mathematical value that can be calculated for any matrix that has a different number of rows and columns. It represents the scaling factor of the linear transformation described by the matrix.

## How is the determinant of a non square matrix calculated?

The determinant of a non square matrix can be calculated using the cofactor expansion method or by using the Laplace expansion method. These methods involve finding the determinant of smaller submatrices within the original matrix.

## What does the determinant of a non square matrix tell us?

The determinant of a non square matrix can tell us whether the matrix is invertible or not. If the determinant is equal to 0, the matrix is not invertible and does not have an inverse. Additionally, the absolute value of the determinant can give us information about the scaling or stretching of the linear transformation described by the matrix.

## Can the determinant of a non square matrix be negative?

Yes, the determinant of a non square matrix can be negative. The determinant can be positive, negative, or zero, depending on the values of the matrix. A negative determinant indicates that the linear transformation described by the matrix involves a reflection or rotation.

## What are some real-world applications of the determinant of a non square matrix?

The determinant of a non square matrix is used in many areas of mathematics and science, such as in linear algebra, physics, and computer graphics. It can be used to solve systems of equations, determine the invertibility of a matrix, and describe transformations in 2D and 3D spaces.

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