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Non-singular matrix

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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.

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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=48004
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article