نتایج جستجو برای: orthogonal basis

تعداد نتایج: 426776  

Journal: :Annals of Global Analysis and Geometry 2011

2005
Ramesh Neelamani Sanjeeb Dash Richard G. Baraniuk

We study ”nearly orthogonal” lattice bases, or bases where the angle between any basis vector and the linear subspace spanned by the other basis vectors is greater than π 3 radians. We show that a nearly orthogonal lattice basis always contains a shortest lattice vector. Moreover, if the lengths of the basis vectors are “nearly equal”, then the basis is the unique nearly orthogonal lattice basi...

In this paper we proved that every g-Riesz basis for Hilbert space $H$ with respect to $K$ by adding a condition is a Riesz basis for Hilbert $B(K)$-module $B(H,K)$. This is an extension of [A. Askarizadeh, M. A. Dehghan, {em G-frames as special frames}, Turk. J. Math., 35, (2011) 1-11]. Also, we derived similar results for g-orthonormal and orthogonal bases. Some relationships between dual fra...

2015
Yuval Filmus

We present a simple, explicit orthogonal basis of eigenvectors for the Johnson and Kneser graphs, based on Young’s orthogonal representation of the symmetric group. Our basis can also be viewed as an orthogonal basis for the vector space of all functions over a slice of the Boolean hypercube (a set of the form {(x1, . . . , xn) ∈ {0, 1} : ∑ i xi = k}), which refines the eigenspaces of the Johns...

2012
Sanjay Govindjee John Strain Toby J. Mitchell Robert L. Taylor

The least-squares projection procedure appears frequently in mathematics, science, and engineering. It possesses the well-known property that a least-squares approximation (formed via orthogonal projection) to a given data set provides an optimal fit in the chosen norm. The orthogonal projection of the data onto a finite basis is typically approached by the inversion of a Gram matrix involving ...

Journal: :Linear Algebra and its Applications 2021

This paper considers theoretical analysis of recovering a low rank matrix given few expansion coefficients with respect to any basis. The current approach generalizes the existing for low-rank completion problem sampling under entry sensing or symmetric orthonormal is based on dual certificates using basis approach. We introduce condition called correlation condition. can be computed in time O ...

Journal: :International Journal of Digital Crime and Forensics 2021

Journal: :CoRR 2008
Alin Bostan Bruno Salvy Éric Schost

We discuss efficient conversion algorithms for orthogonal polynomials. We describe a known conversion algorithm from an arbitrary orthogonal basis to the monomial basis, and deduce a new algorithm of the same complexity for the converse operation.

Journal: :SIAM J. Discrete Math. 2007
Ramesh Neelamani Sanjeeb Dash Richard G. Baraniuk

We study lattice bases where the angle between any basis vector and the linear subspace spanned by the other basis vectors is at least π 3 radians; we denote such bases as “nearly orthogonal.” We show that a nearly orthogonal lattice basis always contains a shortest lattice vector. Moreover, we prove that if the basis vector lengths are “nearly equal,” then the basis is the unique nearly orthog...

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