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Matrix equivalence
About: Matrix equivalence is a research topic. Over the lifetime, 532 publications have been published within this topic receiving 9514 citations.
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01 Jan 1995TL;DR: The Cartan-Kahler existence theorem as discussed by the authors is based on the Cartan's equivalence method, which is a generalization of the Frobenius' theorem of Cartan and Kuhn.
Abstract: 1 Geometric foundations 2 Lie groups 3 Representation theory 4 Jets and contact transformations 5 Differential invariants 6 Symmetries of differential equations 7 Symmetries of variational problems 8 Equivalence of coframes 9 Formulation of equivalence problems 10 Cartan's equivalence method 11 Involution 12 Prolongation of equivalence problems 13 Differential systems 14 Frobenius' theorem 15 The Cartan-Kahler existence theorem
1,078 citations
TL;DR: In this article, it was shown that for any amenable non-singular countable equivalence relation R⊂X×X, there exists a nonsingular transformation T of X such that, up to a null set, any two Cartan subalgebras of a hyperfinite factor are conjugate by an automorphism.
Abstract: We prove that for any amenable non-singular countable equivalence relation R⊂X×X, there exists a non-singular transformation T of X such that, up to a null set:It follows that any two Cartan subalgebras of a hyperfinite factor are conjugate by an automorphism
591 citations
TL;DR: In this article, a complete characterization of the class of nonlinear systems which are equivalent to controllable linear systems is obtained, and an equivalence relation is established for the systems x = f(x, u).
459 citations
Book•
01 Jan 1994
TL;DR: The main notations and conventions of linear spaces are discussed in this article, where Canonical forms of matrices and linear operators of special form multilinear algebra and matrix inequalities are discussed.
Abstract: Main notations and conventions Determinants Linear spaces Canonical forms of matrices and linear operators Matrices of special form Multilinear algebra Matrix inequalities Matrices in algebra and calculus Appendix Bibliography Subject index.
414 citations
354 citations