Results 301 to 310 of about 27,372,603 (325)

Simulating the HeI photoelectron spectrum of Cl₂O with new full-dimensional adiabatic potential energy surfaces of Cl₂O(X̃¹A₁), Cl₂O⁺(X̃²B₁), and Cl₂O⁺(C̃²A₂) and a three-state diabatic potential energy matrix of Cl₂O⁺(òB₂, B̃²A₁, and 2²A₁): a quantum mechanical study

Physical Chemistry Chemical Physics, 2023
The photoelectron spectrum of Cl2O is computed quantum mechanically based on new potential energy surfaces and a diabatic potential energy matrix for the first time.
Zhe Hou, Siting Hou, Changjian Xie, Huixian Han   +3 more
openaire   +1 more source

The Square Root of a 2 × 2 Matrix

, 1980
A basic heuristic principle in linear algebra is that all computations are possible for 2X2 matrices. Thus one can compute inverses, eigenvalues, and eigenvectors by manageable formulas. The purpose of this note is to give a simple formula for the square
B. Levinger
semanticscholar   +1 more source

The Power of the 2 × 2 Matrix: Using 2 × 2 Thinking to Solve Business Problems and Make Better Decisions

, 2005
This article presents a review of the book “The Power of the 2×2 Matrix: Using 2×2 Thinking to Solve Business Problems and Make Better Decisions,” by Alex Lowy and Phil Hood.
H. H. Beam
semanticscholar   +1 more source

The nth Power of a 2 × 2 Matrix

, 1992
If the matrix A is invertible (a = 0, [3 = 0), it is easy to see that (2) holds for all integral values of n. If A is real but its eigenvalues a = p + iq and 3 = p iq are nonreal (q = 0) with some power of them real, say (p + iq)..l = (p -iq)" = r, then,
K. Williams
semanticscholar   +1 more source

Representations for the Drazin Inverse of a 2 x 2 Block Matrix

SIAM Journal on Matrix Analysis and Applications, 2005
Two representations for the Drazin inverse of a $2\times2$ block matrix $M=[{A \atop C}\;{B \atop D}]$, where $A$ and $D$ are square matrices, in terms of the Drazin inverses of $A$ and $D$ have been recently developed under the assumptions that $C(I-AA^{
Robert Hartwig, Xiezhang Li, Yimin Wei
semanticscholar   +1 more source

4 × 4 and 2 × 2 matrix formulations for the optics in stratified and biaxial media

, 1997
Exact matrix representations for refraction and reflection at an interface between arbitrarily oriented biaxial media and for the wave propagation within a biaxial homogeneous medium are derived.
C.-J. Chen, A. Lien, M. Nathan
semanticscholar   +1 more source

Zeros of 2 × 2 Matrix Polynomials

, 2009
Consider the nth degree polynomial equation, X n + A n−1 X n−1 + … +A 1 X + A 0 = 0 over the ring of 2 × 2 complex matrices. If this equation has more than solutions, then it has infinitely many solutions.
M. Slusky
semanticscholar   +1 more source

General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference.

Applied Optics, 2002
The optical response of coherent thin-film multilayers is often represented with Fresnel coefficients in a 2 x 2 matrix configuration. Here the usual transfer matrix was modified to a generic form, with the ability to use the absolute squares of the ...
Charalambos C. Katsidis, D. Siapkas
semanticscholar   +1 more source

Generalized Collinearity Diagnostics

, 1992
Working in the context of the linear model y = Xβ + e, we generalize the concept of variance inflation as a measure of collinearity to a subset of parameters in β (denoted by β 1, with the associated columns of X given by X 1).
J. Fox, G. Monette
semanticscholar   +1 more source