Inverting the sum of two singular matrices

Autor: Sofia Eriksson, Jonas Nordqvist
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: Results in Applied Mathematics, Vol 22, Iss , Pp 100463- (2024)
Druh dokumentu: article
ISSN: 2590-0374
DOI: 10.1016/j.rinam.2024.100463
Popis: Square matrices of the form A˜=A+eDf∗ are considered. An explicit expression for the inverse is given, provided A˜ and D are invertible with rank(A˜)=rank(A)+rank(eDf∗). The inverse is presented in two ways, one that uses singular value decomposition and another that depends directly on the components A, e, f and D. Additionally, a matrix determinant lemma for singular matrices follows from the derivations.
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