Continuity properties of factors in polar decompositions of matrices with respect to inde®nite scalar products are studied. The matrix having the polar decomposition and the inde®nite scalar product are allowed to vary. Closely related properties of a self-adjoint (with respect to an inde®nite scalar product) perturbed matrix to have a self-adjoint square root, or to have a representation of th...

A quantum yield of •i•e = 2.3 x 10 '4 (+_ 4 X 10 -•) was determined for the photochemical degradation of 4nitrophenol over the wavelength range of 300 to 370 nm in ice pellets (pH 5.6). Five reaction products were identified: hydroquinone, benzoquinone, 4-nitrosophenol, nitrate, nitrite, and the likely formation of organic polymers. The similarities of these results to the observations from 4-n...

Let Cm×n, Cm×n r , C m ≥ , C m > , and In denote the set of m × n complex matrices, subset of Cm×n consisting of matrices with rank r, set of the Hermitian nonnegative definite matrices of order m, subset of C ≥ consisting of positive-definite matrices and n × n unit matrix, respectively. Without specification, we always assume that m > n >max{r, s} and the given weight matrices M ∈ C > ,N ∈ C ...

This paper reports the experimental results of a novel method to calibrate geometric errors of multi-axis robotic manipulators. The method proposed by the authors is based on a least-square estimation of the rotation matrix of a rigid body in three-dimensional Cartesian space. The error is filtered by hnposing the orthogonality constraint on the rotation matrix, using the polar-decomposition th...

The Mueller matrix describes all the polarizing properties of a sample and, therefore, the optical differences between noncancerous and precancerous tissue that may be present within the matrix elements. A high-speed polarimetry system that generates 16 (4x4) full Mueller matrices to characterize tissues is presented. Feature extraction is done on the Mueller matrix elements resulting in depola...

Point pattern matching (PPM) is an important problem in pattern recognition, digital video processing and computer vision. In this paper, novel and fast procedure based on Genetic Algorithm, for afine PPM is described. Most matching techniques solved the PPM problem by determining the correspondence between points localized spatially within two sets, then to get the proper transformation parame...

Let A be a unital C -algebra with involution represented in a Hilbert space H, G the group of invertible elements of A, U the unitary group of A, G the set of invertible selfadjoint elements of A, Q = f" 2 G : " = 1g the space of re ections and P = Q \ U . For any positive a 2 G consider the a-unitary group Ua = fg 2 G : a g a = g g, i.e., the elements which are unitary with respect to the scal...

The changes in the unitary polar factor under both multiplicative and additive perturbation are studied. A multiplicative perturbation bound and a new additive perturbation bound, in which a different measure of perturbation is introduced, are presented. AMS subject classification (2000): 15A18, 15A23, 65F35.

We introduce a dynamically weighted Halley (DWH) iteration for computing the polar decomposition of a matrix, and prove that the new method is globally and asymptotically cubically convergent. For matrices with condition number no greater than 1016, the DWH method needs at most 6 iterations for convergence with the tolerance 10−16. The Halley iteration can be implemented via QR decompositions w...

This paper presents a method to decompose binary shapes into connected parts, based on their structure, as captured by the eccentricity transform. This decomposition is then used in a graph pyramid framework for mapping a polar-like coordinate system to a non-rigid shape. Initial experimental results are presented.