# Can you have a determinant of a non-square matrix?

## Can you have a determinant of a non-square matrix?

For non-square matrices, there is no determinant value. Determinant of matrix is calculated only for square matrices.

Can non-square matrices be similar?

Two similar matrices are not equal, but they share many important properties. Definition (Similar Matrices) Suppose A and B are two square matrices of size n . Then A and B are similar if there exists a nonsingular matrix of size n , S , such that A=S−1BS A = S − 1 B S .

### Are non-square matrices Diagonalizable?

Every matrix is not diagonalisable. Take for example non-zero nilpotent matrices. The Jordan decomposition tells us how close a given matrix can come to diagonalisability.

Is there a determinant for a non square matrix?

There is no deﬁnition of determi- nant for non square matrices. T o break this we in troduced a new concept called non inverse of the non square matrices. 2. Non Square Determinant Deﬁnition 2.1 : Let A be a non square matrix of order m × n.

#### Can a non-square matrix have both left and right inverses?

A matrix has a right inverse if and only if it has linearly independent rows. So a reason why a non-square matrix cannot have both a left and a right inverse becomes apparent: a non-square matrix cannot have linearly independen They can have left-inverses, or right-inverses, but they cannot have inverses.

Is the op interested in non-square matrices?

I wrote an answer to this question based on determinants, but subsequently deleted it because the OP is interested in non-square matrices, which effectively blocks the use of determinants and thereby undermined the entire answer.

## Is there a function Det on all square matrices?

However, it can be salvaged if there exists a function det defined on all real-valued matrices (not just the square ones) having the following properties. det ( A B) always equals det ( A) det ( B) whenever the product A B is defined. Does such a function exist? Such a function cannot exist. Let A = ( 1 0 0 1 0 0) and B = ( 1 0 0 0 1 0).