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Matrices as Sums of Invertible Matrices

by N. J. Lord (Tonbridge School, England)

This article originally appeared in:
Mathematics Magazine
February, 1987

Subject classification(s): Algebra and Number Theory | Abstract Algebra | Fields | Linear Algebra | Matrix Algebra
Applicable Course(s): 4.13 Advanced Linear Algebra

The author shows that any square matrix over a field is the sum of two invertible matrices, and that the decomposition is unique only if the matrix is nonzero and of size 2x2 with entries in the field of two elements.

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