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- Title
Determinantal Representation of Outer Inverses in Riemannian Space.
- Authors
Stanimirović, Predrag S.; Zlatanović, Milan Lj.
- Abstract
Starting from a known determinantal representation of outer inverses, we derive their determinantal representation in terms of the inner product in the Euclidean space. We define the double inner product of two miscellaneous tensors of rank 2 in a Riemannian space. The corresponding determinantal representation as well as the general representation of outer inverses in the Riemannian space are derived. A non-zero {2}-inverse X of a given tensor A obeying ρ(X) = s with 1 ≤ s ≤ r = ρ(A) is expressed in terms of the double inner product involving compound tensors with minors of order s, extracted from A and appropriate tensors.
- Subjects
DETERMINANTAL rings; RIEMANNIAN manifolds; EUCLIDEAN geometry; TENSOR algebra; INVERSE Galois theory; INFORMATION theory
- Publication
Algebra Colloquium, 2012, Vol 19, p877
- ISSN
1005-3867
- Publication type
Article