Subspaces and Cosets of Subspace of Real Unitary Space

Operations on Subspaces in Real Unitary Space

Let V be a real unitary space and let W1, W2 be subspaces of V . The functor W1 + W2 yields a strict subspace of V and is defined as follows: (Def. 1) The carrier of W1 + W2 = {v + u; v ranges over vectors of V , u ranges over vectors of V : v ∈ W1 ∧ u ∈ W2}. Let V be a real unitary space and let W1, W2 be subspaces of V . The functor W1 ∩ W2 yields a strict subspace of V and is defined by: (De...

Isotropic Constant Dimension Subspace Codes

 In network code setting, a constant dimension code is a set of k-dimensional subspaces of F nq . If F_q n is a nondegenerated symlectic vector space with bilinear form f, an isotropic subspace U of F n q is a subspace that for all x, y ∈ U, f(x, y) = 0. We introduce isotropic subspace codes simply as a set of isotropic subspaces and show how the isotropic property use in decoding process, then...

ε-weakly Chebyshev subspaces and quotient spaces

Invariant subspaces in Simpira

In this short note we report on invariant subspaces in Simpira in the case of four registers. In particular, we show that the whole input space (respectively output space) can be partitioned into invariant cosets of dimension 56 over F 28 . These invariant subspaces are found by exploiting the non-invariant subspace properties of AES together with the particular choice of Feistel configuration....

Weak*-closed invariant subspaces and ideals of semigroup algebras on foundation semigroups

Let S be a locally compact foundation semigroup with identity and                          be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of    In this paper, we prove that  X  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenab...