For the inverse of a matrix A, A-1, we have A A-1 = A-1 A = I, where I is the identity matrix.
| · | A matrix has an inverse only if its determinant is not zero. |
| · | Only square matrices have inverses. |
A square matrix for which there exists no inverse is known as a singular matrix; a matrix for which there exists an inverse is an invertible or non-singular matrix.
A matrix for which all principal minors are different from zero is termed strongly non-singular.
The rank of a square matrix A is defined as the size of the largest square sub-matrix of A that is non-singular.
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