Non-singular matrix

non-degenerate matrix

A square matrix with non-zero determinant. For a square matrix $A$ over a field, non-singularity is equivalent to each of the following conditions: 1) $A$ is invertible; 2) the rows (columns) of $A$ are linearly independent; or 3) $A$ can be brought by elementary row (column) transformations to the identity matrix.

References

[a1]	A.G. Kurosh, "Matrix theory" , Chelsea, reprint (1960) (Translated from Russian)
[a2]	B.R. McDonald, "Linear algebra over commutative rings" , M. Dekker (1984)