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Row Rank Equals Column Rank

by William P. Wardlaw (U. S. Naval Academy)

This article originally appeared in:
Mathematics Magazine
October, 2005

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

A short elementary proof of the equality of row rank and column rank is given. The proof requires only the definition of matrix multiplication and the fact that a minimal spanning set is a basis.

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Capsule Course Topic(s):
Linear Algebra | Rank of Matrices
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