# On Uniformly Filled Determinants

by Herbert S. Wilf (University of Pennsylvania) and Carsten Thomassen (University of Pennsylvania)

College Mathematics Journal
March, 1990

Subject classification(s): Algebra and Number Theory | Linear Algebra
Applicable Course(s): 3.8 Linear/Matrix Algebra | 4.13 Advanced Linear Algebra

Given a square matrix $U$ and column vectors $\alpha$ and $\beta$, the author shows that $\det(U + \alpha \beta^T) = \det U + \beta^T$ Cof$(U) \alpha$.  This capsule responds to and generalizes a previous classroom capsule.

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Capsule Course Topic(s):
Linear Algebra | Determinants