determinants of some matrices of special form


Suppose A is n×n square matrixMathworldPlanetmath, u,v are two column n-vectors, and α is a scalar. Then

det(A+uvT) = detA+vTadjAu,
det(AuvTα) = αdetA-vTadjAu,

where adjA is the adjugatePlanetmathPlanetmath of A.

References

Title determinants of some matrices of special form
Canonical name DeterminantsOfSomeMatricesOfSpecialForm
Date of creation 2013-03-22 14:03:41
Last modified on 2013-03-22 14:03:41
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 5
Author bwebste (988)
Entry type Result
Classification msc 15A15
Related topic BlockDeterminants