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When is Rank Additive?

by David Callan (University of Wisconsin)

This article originally appeared in:
College Mathematics Journal
March, 1998

Subject classification(s): Algebra and Number Theory | Algebra | Matrices
Applicable Course(s): 3.8 Linear/Matrix Algebra

This capsule presents necessary and sufficient conditions for the matrix rank of a sum to be the sum of the ranks.  The crux of the argument uses the fact that the rank of a matrix is the size of its largest invertible submatrix.

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Capsule Course Topic(s):
Linear Algebra | Bases
Linear Algebra | Linear Independence
Linear Algebra | Matrix Algebra
Linear Algebra | Rank of Matrices
Linear Algebra | Vector Spaces, Subspaces
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