Transformations of the form A ! C 1 AC 2 are investigated that transform Toeplitz and Toeplitz-plus-Hankel matrices into generalized Cauchy matrices. C 1 and C 2 are matrices related to the discrete Fourier transformation or to various real trigonometric transformations. Combining these results with pivoting techniques,in part II algorithmsfor Toeplitz and Toeplitz-plus-Hankel systems will be p...

Calibration of a structured light system is considered in this paper. The system consists of a projector whose output is controlled by a liquid crystal shutter, and a camera to capture the images. A sequence of patterns is projected to temporally encode 256 stripes on the visible surfaces. The transformation from 3D world coordinates to camera image plane coordinates and projector stripe ids ar...

Calibration of a structured light system is considered in this paper. The system consists of a projector whose output is controlled by a liquid crystal shutter, and a camera to capture the images. A sequence of patterns is projected to temporally encode 256 stripes on the visible surfaces. The transformation from 3D world coordinates to camera image plane coordinates and projector stripe ids ar...

We present a new fast and efficient algorithm for computing the eigenvalues and eigenvectors of large-size nondefective complex symmetric matrices. Our work was motivated by the emergence of this problem in recent methods for solving chemical reactive problems. The algorithm we present is similiar to the QR (QL) algorithm for complex Hermitian matrices, but we use complex orthogonal (not unitar...

The contragredient transformation A 7→ PAP, B 7→ PBP of two matrices A,B effects simultaneous similarity transformations of the products AB and BA. This work provides structured canonical forms under this transformation for symmetric or skew-symmetric A,B. As an application, these forms are used to study the quadratic matrix equation XAX = B, where both A,B are skew-symmetric or symmetric matri...

The contragredient transformation A 7→ PAP, B 7→ PBP of two matrices A,B effects simultaneous similarity transformations of the products AB and BA. This work provides structured canonical forms under this transformation for symmetric or skew-symmetric A,B. As an application, these forms are used to study the quadratic matrix equation XAX = B, where both A,B are skew-symmetric or symmetric matri...

The contragredient transformation A 7→ P−1AP−T, B 7→ PTBP of two matrices A,B effects simultaneous similarity transformations of the products AB and BA. This work provides structured canonical forms under this transformation for symmetric or skew-symmetric A,B. As an application, these forms are used to study the quadratic matrix equation XAX = B, where both A,B are skew-symmetric or symmetric ...

Transformation matrices of the weights of the atomic wave functions in jj coupling to the relevant weights of LS coupling are considered for a shell of equivalent electrons. Their use allows one to preserve main part of relativistic effects but to classify the energy levels of an atom or an ion considered with the help of a set of quantum numbers of LS coupling scheme. Having in mind that the n...

Let L̂ be a positive definite bilinear functional on the unit circle defined on Pn, the space of polynomials of degree at most n. Then its Geronimus transformation L is defined by L̂(p, q) = L ( (z − α)p(z), (z − α)q(z) ) for all p, q ∈ Pn, α ∈ C. Given L̂, there are infinitely many such L which can be described by a complex free parameter. The Hessenberg matrix that appears in the recurrence rela...

Symmetric Positive Definite (SPD) matrices have been widely used for data representation in many visual recognition tasks. The success mainly attributes to learning discriminative SPD matrices with encoding the Riemannian geometry of the underlying SPD manifold. In this paper, we propose a geometry-aware SPD similarity learning (SPDSL) framework to learn discriminative SPD features by directly ...