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Linear Algebra and its Applications 429 (2008) 21362145 www.elsevier.com/locate/laa
 

Summary: Linear Algebra and its Applications 429 (2008) 2136­2145
www.elsevier.com/locate/laa
On singular values of partially prescribed matrices
Pedro M.Q. Aguiar, Marko Stosi´c
, João Xavier
Instituto de Sistemas e Robótica, Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal
Received 31 August 2007; accepted 9 June 2008
Available online 3 August 2008
Submitted by J.F. Queiró
Abstract
In this paper we study singular values of a matrix whose one entry varies while all other entries are
prescribed. In particular, we find the possible pth singular value of such a matrix, and we define explicitly
the unknown entry such that the completed matrix has the minimal possible pth singular value. This in turn
determines possible pth singular value of a matrix under rank one perturbation. Moreover, we determine the
possible value of pth singular value of a partially prescribed matrix whose set of unknown entries has a form
of a Young diagram. In particular, we give a fast algorithm for defining the completion that minimizes the
pth singular value of such matrix.
© 2008 Elsevier Inc. All rights reserved.
AMS classification: 15A18
Keywords: Singular value; Matrix completion; Rank deficiency matrix

  

Source: Aguiar, Pedro M. Q. - Institute for Systems and Robotics (Lisbon)
Institute for Systems and Robotics, Lisboa

 

Collections: Engineering