How to verify whether the matrix of a non-square matrix is reversible

How can we prove whether the matrix of a non-square matrix is reversible?

1. It is generally used to define the inverse matrix of the square matrix and to study whether the square matrix is reversible or inverse;

2. For non-square arrays, such as C (m x N) and M = N, the product of C and its transpose matrix C is usually defined:

   The inverse matrix of T = CC' (m-Order Matrix) or T = C' C (n-order matrix) is the 'generalized inverse matrix 'of the C-matrix '.

3. For example, the generalized inverse matrix defined in (2) always exists when | T | =0. The proof method is the same as that of the square array.

4. Example: c = 1, 2, 3

   Row 2: 3, 2, 1

   C transpose C': 1, 3

   Row 2: 2

   Row 3: 3, 1

   T = CC': 14,10

   Row 2: 10, 14. The inverse matrix of T exists, because: | T | ≠ 0.