in the linear system ax = b the points x are sometimes constrained to lie in a given subspace s of column space of a. drazin inverse for any singular or nonsingular matrix, exist and is unique. in this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of drazin inverse in solving such systems is investigated. constrained linear system arise ...

It is a common practice that a matrix, the de facto image representation, is first converted into a vector before fed into subspace analysis or kernel method; however, the conversion ruins the spatial structure of the pixels that defines the image. In this paper, we propose two kernel subspace methods that are directly based on the matrix representation, namely matrix-based kernel principal com...

Given a square matrix A, the inverse subspace problem is concerned with determining a closest matrix to A with a prescribed invariant subspace. When A is Hermitian, the closest matrix may be required to be Hermitian. We measure distance in the Frobenius norm and discuss applications to Krylov subspace methods for the solution of large-scale linear systems of equations and eigenvalue problems as...

A QR based technique is presented for estimating the approximate numerical rank and corresponding signal subspace of a matrix together with the subspace projection of the least squares weights. Theoretical difficulties associated with conventional QR factorisation are overcome by applying the technique of RowZeroing QR to the covariance matrix. Thresholding is simplified compared with the use o...

Many signal processing algorithms are based on the computation of the eigenstructure (eigenvalues and eigenvectors) of the covariance matrix of a data matrix. Applications include: direction of arrival estimation in array processing, spectral estimation and CDMA synchronization [1]. The advantages of using the eigenvector-based methods (also called subspace based methods) are well-known. In the...