mathguy34 said:I need help proving the following:
1 A non-square matrix cannot have both a left and a right inverse
2 If a non-square matrix has a left(right) inverse, it has infinitely many.
3 If m<n, a non-square matrix has a right inverse if and only if rank A=m
Non-square matrices are matrices that do not have an equal number of rows and columns. They can have any number of rows and columns, as long as the number of rows is not equal to the number of columns.
To prove properties of non-square matrices, we can use different methods such as finding determinants, calculating eigenvalues and eigenvectors, and performing matrix operations such as addition, subtraction, and multiplication.
The determinant of a non-square matrix is a scalar value that represents the matrix's size and shape. It is calculated by multiplying the elements of the matrix and then subtracting the product of the elements in the opposite diagonal.
No, non-square matrices do not have inverse matrices. Only square matrices with a non-zero determinant have inverse matrices.
Non-square matrices are commonly used in computer graphics, data analysis, and statistics. They can also be used to represent and manipulate data in scientific and engineering calculations.