# Non-singular matrix

From Encyclopedia of Mathematics

*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) |

**How to Cite This Entry:**

Non-singular matrix.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Non-singular_matrix&oldid=53854

This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article