Two canonical forms for skew-symmetric matrix polynomials over arbitrary fields are characterized — the Smith form, and its skew-symmetric variant obtained via unimodular congruences. Applications include the analysis of the eigenvalue and elementary divisor structure of products of two skew-symmetric matrices, the derivation of a Smith-McMillan-like canonical form for skew-symmetric rational m...

It is well known that the matrix exponential function has practical applications in engineering and applied sciences. In this paper, we present some new explicit identities to the exponential functions of a special class of matrices that are known as central-symmetric $X$-form. For instance, $e^{mathbf{A}t}$, $t^{mathbf{A}}$ and $a^{mathbf{A}t}$ will be evaluated by the new formulas in this par...

Photons experience mirror asymmetry of macroscopic chiral media, as in circular dichroism and polarization rotation, since left- right-handed polarizations differently couple with matter handedness. Conversely, free relativistic electrons vanishing orbital angular momentum have no handedness so the question arises whether they can sense chirality geometrically symmetric samples. In this paper, ...

A solution of the problem of calculating cartesian coordinates from a matrix of interpoint distances (the embedding problem) is reported. An efficient and numerically stable algorithm for the transformation of distances to coordinates is then obtained. It is shown that the embedding problem is intimately related to the theory of symmetric matrices, since every symmetric matrix is related to a g...

Object recognition under varying pose is a challenging problem, especially when illumination variations are also present. In this paper, we propose a pose-normalized view synthesis method under varying illuminations for symmetric objects. For a given non-frontal view of a symmetric object under non-frontal illumination, the mirror image of the original view is equivalent to the view when the ob...

The analysis of spatial structure, ie, the encoding of relative positions between pattern elements, was studied in central and eccentric vision. In a two-alternative forced-choice task the observer had to discriminate between two patterns consisting of short line segments. At each trial the two patterns were flashed for 140 msec and the observer indicated whether the patterns were identical or ...

The (sqrt[3]×sqrt[3])R30° honeycomb of silicene monolayer on Ag(111) was found to undergo a phase transition to two types of mirror-symmetric boundary-separated rhombic phases at temperatures below 40 K by scanning tunneling microscopy. The first-principles calculations reveal that weak interactions between silicene and Ag(111) drive the spontaneous unusual buckling in the monolayer silicene, f...

The role of bilateral symmetry in face recognition is investigated in two psychophysical experiments using a Same/Different paradigm. The results of Experiment 1 confirm the hypothesis that the ability to identify mirror symmetric patterns is used for viewpoint generalization by approximating the view symmetric to the learned view by its mirror reversed image. The results of Experiment 2 show t...

In this paper we construct the symmetric quasi anti-bidiagonal matrix that its eigenvalues are given, and show that the problem is also equivalent to the inverse eigenvalue problem for a certain symmetric tridiagonal matrix which has the same eigenvalues. Not only elements of the tridiagonal matrix come from quasi anti-bidiagonal matrix, but also the places of elements exchange based on some co...