Inversion of Circulant Matrices over Zm
... Toeplitz matrices with entries over the ring Zm . In addition to their own interest as linear algebra problems, these problems play an important role in the theory of linear Cellular Automata. The standard algorithm for inverting circulant matrices with real or complex entries is based on the fact t ...
... Toeplitz matrices with entries over the ring Zm . In addition to their own interest as linear algebra problems, these problems play an important role in the theory of linear Cellular Automata. The standard algorithm for inverting circulant matrices with real or complex entries is based on the fact t ...
19. Basis and Dimension
... everywhere else is written ei . It points in the direction of the ith coordinate axis, and has unit length. In multivariable calculus classes, this basis is often written {i, j, k} for R3 . Bases are not unique. While there exists a unique way to express a vector in terms of any particular basis, b ...
... everywhere else is written ei . It points in the direction of the ith coordinate axis, and has unit length. In multivariable calculus classes, this basis is often written {i, j, k} for R3 . Bases are not unique. While there exists a unique way to express a vector in terms of any particular basis, b ...
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... • Permutation representations: let X be a finite set on which G acts (on the left). Let VX := ⊕x∈X Cex . A natural action of G on VX is given by gex = egx , and defines a representation of G, of degree |X| the cardinal of X. The matrices of this representation (in the basis {ex }) are permutation ma ...
... • Permutation representations: let X be a finite set on which G acts (on the left). Let VX := ⊕x∈X Cex . A natural action of G on VX is given by gex = egx , and defines a representation of G, of degree |X| the cardinal of X. The matrices of this representation (in the basis {ex }) are permutation ma ...
SOME PROPERTIES OF N-SUPERCYCLIC OPERATORS 1
... a simple eigenvalue for T ⊕ I with corresponding eigenvector 0 ⊕ 1. (Thus, the adjoint of a supercyclic operator on an infinite-dimensional space may have a simple eigenvalue.) Now, consider T ⊕I ⊕I : `2 ⊕C⊕C → `2 ⊕C⊕C. We claim that S := T ⊕I ⊕I is 2-supercyclic with supercyclic subspace spanned by ...
... a simple eigenvalue for T ⊕ I with corresponding eigenvector 0 ⊕ 1. (Thus, the adjoint of a supercyclic operator on an infinite-dimensional space may have a simple eigenvalue.) Now, consider T ⊕I ⊕I : `2 ⊕C⊕C → `2 ⊕C⊕C. We claim that S := T ⊕I ⊕I is 2-supercyclic with supercyclic subspace spanned by ...
Tensors, Vectors, and Linear Forms Michael Griffith May 9, 2014
... multilinear form with m arguments. Third, multiplication of two tensors is performed by summing the product of their entries over some shared index. We have seen this in the action of linear operators. The third point is an important one, as it implies that the action of a rank(n,m) tensor sends a r ...
... multilinear form with m arguments. Third, multiplication of two tensors is performed by summing the product of their entries over some shared index. We have seen this in the action of linear operators. The third point is an important one, as it implies that the action of a rank(n,m) tensor sends a r ...