Examples are given of modules V with fln(V)∈{0,1,∞}. C. J. Maxson and A. Kreuzer have demonstrated that fln(V)=2 is possible [Forcing linearity numbers for injective modules over PID's (Preprint, 1998)], and the authors have shown that fln(V)=q+2 if V is a vectorspace of...
Determine if the described set is a subspace. If so, give proof. If not, explain why not. Unless stated otherwise, a, b, and c are real numbers. This is a linear algebra problem. The subset of R^2 Prove that if U and W ...
In the present paper, we study the behavior relative to this notion of one of the currently most important examples of vectorial functions for cryptography, namely the (multiplicative) inverse function, defined over \mathbb {F}_{2^n} as F(x)=x^{2^n-2}, that is, F(x)=\frac{1}{x...
ICF Ipsen - 《Linear Algebra & Its Applications》 被引量: 61发表: 2000年 Canonical analysis relative to a closed subspace First a maximum coefficient notion between two real closed Hilbertian subspaces relative to a third one is given. Many examples illustrate the study when t... J Dauxois,...
Prove this linear algebra problem. Please show all work. Let V and W be subspaces of Rn such that V ⊂ W. Show that W⊥⊂V⊥. Orthogonal complement: A subspace V is said to orthogonal complement of a set W if ...
Inspired by the quantum computing algorithms for Linear Algebra problems [HHL,TaShma] we study how the simulation on a classical computer of this type of "... M Ben-Or,L Eldar - 《Computer Science》 被引量: 2发表: 2015年 Hyperinvariant subspaces for sets of polynomially compact operators ...
In this paper we use Num 1 to give a characterization of hermitian matrices, give some examples of 3 × 3 matrices M with Num k ( M ) = F q 2 for all k ∈ F q and study F q and F q 2 linear subspaces V M n , n ( F q 2 ) such that either ( Num 1 ( M ) ) ≤...
,Mzn) of multiplication operators with the coordinate functions on these reproducing kernel Hilbert spaces are examples of pure commuting contractive tuples of operators. Let K be a positive definite function on Bn holomorphic in the first and anti-holomorphic in the second variable. Then the ...
As a consequence, we obtain examples of non-square MRD codes which are not equivalent to generalized Gabidulin or twisted Gabidulin codes. We show that, up to equivalence, MRD codes having the same parameters as the ones in our connection come from an h-scattered subspace. Also, we ...
Further examples of the “linear algebraic” view are given by the following definitions and proposition. Given the reaction vectors for a reaction network (\mathscr {S},\mathscr {C},\mathscr {R}) that are the members of the set \{y' - y \in \mathbb {R}^\mathscr {S}: y \rightar...