Generating a d-dimensional Linear Subspace Efficiently

نویسنده

  • Raphael Yuster
چکیده

We present an algorithm for computing a d-dimensional subspace of the row space of a matrix. For an n×n matrix A with m nonzero entries and with rank(A) ≥ d the algorithm generates a d × n matrix with full row rank and which is a subspace of Rows(A). If rank(A) < d the algorithm generates a rank(A)×n row-equivalent matrix. The running time of the algorithm is

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Subspace-diskcyclic sequences of linear operators

A sequence ${T_n}_{n=1}^{infty}$ of bounded linear  operators on a separable infinite dimensional Hilbert space $mathcal{H}$ is called subspace-diskcyclic with respect to the closed subspace $Msubseteq mathcal{H},$ if there exists a vector $xin mathcal{H}$ such that the disk-scaled orbit ${alpha T_n x: nin mathbb{N}, alpha inmathbb{C}, | alpha | leq 1}cap M$ is dense in $M$. The goal of t...

متن کامل

Extending Mehrotra's Corrector for Linear Programs

In this article a primal-dual interior-point method for solving linear programs is proposed. A new approach for generating higher-order search directions, and a new method for an eecient higher-order subspace search along several search directions are the basis of the proposed extension. The subspace search is reduced to a linear program in several variables. The method using the simplest (two-...

متن کامل

Efficient Point-to-Subspace Query in $\ell^1$: Theory and Applications in Computer Vision

Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of low-dimensional linear subspaces in a high-dimensional ambient (image) space and a query point (image), efficiently determine the nearest subspace to the query in ` distance. We show in theory that Cauchy random embedding of the objects into significantlylower-d...

متن کامل

Efficient Point-to-Subspace Query in ℓ1: Theory and Applications in Computer Vision

Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of low-dimensional linear subspaces in a high-dimensional ambient (image) space and a query point (image), efficiently determine the nearest subspace to the query in ` distance. We show in theory that Cauchy random embedding of the objects into significantlylower-d...

متن کامل

The p-Rank of the Incidence Matrix of Intersecting Linear Subspaces

Let V be a vector space of dimension n+1 over a field of p elements. A d-dimensional subspace and an e-dimensional subspace are considered to be incident if their intersection is not the zero subspace. The rank of these incidence matrices, modulo p, are computed for all n, d, e and t. This result generalizes the well known formula of Hamada for the incidence matrices between points and subspace...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010