%0 Journal Article
%T Constrained Low Rank Approximation of the Hermitian Nonnegative-Definite Matrix
%A Haixia Chang
%J Advances in Linear Algebra & Matrix Theory
%P 22-33
%@ 2165-3348
%D 2020
%I Scientific Research Publishing
%R 10.4236/alamt.2020.102003
%X <span style=\"line-height:1.5;\"><span>In this paper, we consider a
constrained low rank approximation problem: </span><img src=\"Edit_57d85c54-7822-4512-aafc-f0b0295a8f75.png\" width=\"100\" height=\"24\" alt=\"\" /></span><span style=\"line-height:1.5;\"><span>, where </span><i><span>E</span></i><span> is a given complex matrix, </span><i><span>p</span></i><span> is a
positive integer, and </span></span><span style=\"line-height:1.5;\"></span><span style=\"line-height:1.5;\"><span> is the set of
the Hermitian nonnegative-definite least squares solution to the matrix
equation </span><img src=\"Edit_ced08299-d2dc-4dbb-907a-4d8d36d2e87a.png\" width=\"60\" height=\"16\" alt=\"\" /></span><span style=\"line-height:1.5;\"><span>. We discuss the range of </span><i><span>p</span></i><span> and derive the corresponding explicit solution expression of the
constrained low rank approximation problem by matrix decompositions. And an
algorithm for the problem is proposed and the numerical example is given to
show its feasibility.
%K Low Rank Approximation
%K Hermitian Matrix
%K Nonnegative-Definite Matrix
%K Least Square
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=101146