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praharmitra
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Is there a definition of 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.
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.
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.
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.
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.