Determinantal identities over commutative semirings

We present a development of determinantal identities over commutative semirings. This includes a generalization of the Cauchy–Binet and Laplace Theorems, as well as results on compound matrices and adjoints. It is further shown that Laplace's Theorem is a special case of the grade- s-adjoint id...

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Bibliographic Details
Published in:Linear algebra and its applications 2004-08, Vol.387, p.99-132
Main Authors: Poplin, Phillip L, Hartwig, Robert E
Format: Article
Language:English
Subjects:
Algebra
Cauchy–Binet
Determinant
Exact sciences and technology
Laplace
Linear and multilinear algebra, matrix theory
Mathematics
Sciences and techniques of general use
Semiring
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Summary:We present a development of determinantal identities over commutative semirings. This includes a generalization of the Cauchy–Binet and Laplace Theorems, as well as results on compound matrices and adjoints. It is further shown that Laplace's Theorem is a special case of the grade- s-adjoint identity.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2004.02.019