Determinantal identities over commutative semirings
Copyright policy )Determinantal identities over commutative semirings
The authors present a development of determinantal identities over commutative semirings. This includes the following themes: 1. Positive and negative determinants; 2. Determinantal identities; 3. Adjoint matrix identities; 4. A generalization of the Cauchy-Binet theorem; 5. Compound matrices; 6. Identities over semirings; 7. Laplace's expansion over semiring and the Laplace theorem. There are many examples in the paper.
- North Carolina State University United States
- Longwood University United States
- North Carolina Agricultural and Technical State University United States
- South Carolina State University United States
adjoint matrix identities, Numerical Analysis, Semiring, Algebra and Number Theory, Matrices over special rings (quaternions, finite fields, etc.), Determinant, Laplace theorem, Laplace, Matrix equations and identities, Determinants, permanents, traces, other special matrix functions, Endomorphism rings; matrix rings, determinant, commutative semirings, Cauchy–Binet, Discrete Mathematics and Combinatorics, Geometry and Topology, Cauchy-Binet theorem, compound matrices, determinantal identities
adjoint matrix identities, Numerical Analysis, Semiring, Algebra and Number Theory, Matrices over special rings (quaternions, finite fields, etc.), Determinant, Laplace theorem, Laplace, Matrix equations and identities, Determinants, permanents, traces, other special matrix functions, Endomorphism rings; matrix rings, determinant, commutative semirings, Cauchy–Binet, Discrete Mathematics and Combinatorics, Geometry and Topology, Cauchy-Binet theorem, compound matrices, determinantal identities
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