Showing papers on "Orthogonal complement published in 2000"
TL;DR: In this paper, the authors studied orthogonal polynomials with respect to the bilinear form.f;g/SDV.f/AV.g/T Chu;f.N/ g.n/ i;
Abstract: In this paper, we study orthogonal polynomials with respect to the bilinear form .f;g/SDV.f/AV.g/ T Chu;f .N/ g .N/ i;
5 citations
TL;DR: In this article, the concept of maximally orthogonal complementary subspaces was introduced and derived for generalized inverses of linear transformations, which can be used to compute the desired generalized inverse.
1 citations
TL;DR: In this article, the authors characterized Commutative H*-algebra in terms of the property that the orthogonal complement of a right ideal is a left ideal, which is the property of the right ideal.
Abstract: Commutative H*-algebra is characterized in terms of the property that the orthogonal complement of a right ideal is a left ideal.
1 citations
TL;DR: In this article, the authors constructed a bilinear solution of the quantum wave equation on Dθ×Dθ, where D is a dense linear subspace in the Fock space of the free in-field.
Abstract: We construct the solution φ(t,x) of the quantum wave equation □φ+m2φ+λ:φ3:=0 as a bilinear form which can be expanded over Wick polynomials of the free in-field, and where :φ3(t,x): is defined as the normal ordered product with respect to the free in-field. The constructed solution is correctly defined as a bilinear form on Dθ×Dθ, where Dθ is a dense linear subspace in the Fock space of the free in-field. On Dθ×Dθ the diagonal of the Wick symbol of this bilinear form satisfies the nonlinear classical wave equation.
TL;DR: The double angle theorems of Davis and Kahan as discussed by the authors do not directly bound the difference between the old invariant subspace S and the new one S but instead bound S and its reflection J S where the mirror is S and J reverses S ⊥, the orthogonal complement of S. The double angle bounds are proportional to the departure from the identity and from orthogonality of the matrix D = def D −1 JDJ.