Non-singular matrix
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
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
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