Sentence examples for be a linear manifold from inspiring English sources

Let X, Y be Banach spaces, A be a linear manifold in the product space (Xtimes Y), S be a set in X and (yin Y).

Let X and Y be Banach spaces, and A be a linear manifold (or linear subspace) in the product space (Xtimes Y).

Let X and Y be Banach spaces, A be a linear manifold in the product space (Xtimes Y) and P be an algebraic projection from Y onto (A ( theta )).

Let X and Y be Banach spaces, (Asubset Xtimes Y) be a linear manifold, (N ( A )) and (R ( A ) ) be Chebyshev subspaces in X and Y, respectively, (pi_{N ( A ) }:Xrightarrow N ( A ) ) and (pi_{R ( A ) }:Yrightarrow R ( A ) ) be the metric projectors.

Let L be a linear manifold in (Xtimes Y), or, equivalently, the graph of a multi-valued linear operator from X to Y and let S be a prescribed hyperplane in X, i.e. (S=g+N), we denote (A:=L|_{N}).

Let X and Y be Banach spaces, L be a linear manifold in (Xtimes Y), or, equivalently, the graph of a multi-valued linear operator from X to Y, and let S be a prescribed hyperplane in X, i.e. (S=g+N).

An AS is a linear manifold of the stochastic space characterized by maximal response variation.

We therefore seek principled approaches to unsupervised data introspection which are nonlinear (since microarray data distributions are unlikely to be distributed on a linear manifold in high dimensional spaces).

A linear manifold or a subspace ℒ in K is called indefinite if it contains both positive and negative elements.

A pre-requisite for the prediction of the equivalent one-port acoustic source parameters of an engine manifold is a linear mathematical model of the breathing noise generation mechanism at the valves.

A representative of these methods is the eigenvoice method[1], where the low-dimensional manifold is a linear subspace and a set of linear bases (called eigenvoices), which capture most of the variance of the SD model parameters, can be obtained by principal component analysis.