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When successive powers of a matrix T become small (that is, when all of the entries of T approach zero, upon raising T to successive powers), the matrix T converges to the zero matrix. A regular splitting of a non-singular matrix A results in a convergent matrix T. A semi-convergent splitting of a matrix A results in a semi-convergent matrix T.
A matrix effect value of less than 100 indicates suppression, while a value larger than 100 is a sign of matrix enhancement. An alternative definition of matrix effect utilizes the formula: M E = 100 ( A ( e x t r a c t ) A ( s t a n d a r d ) ) − 100 {\displaystyle ME=100\left({\frac {A(extract)}{A(standard)}}\right)-100}
Molecular structures are graphs with chemical constraints such as valences, bond multiplicity and fragments. These generators are the core of CASE systems. In a generator, the molecular formula is the basic input. If fragments are obtained from the experimental data, they can also be used as inputs to accelerate structure generation.
Synonym for binary matrix or logical matrix. Alternant matrix: A matrix in which successive columns have a particular function applied to their entries. Alternating sign matrix: A square matrix with entries 0, 1 and −1 such that the sum of each row and column is 1 and the nonzero entries in each row and column alternate in sign. Anti-diagonal ...
Matrix congruence is an equivalence relation. Matrix congruence arises when considering the effect of change of basis on the Gram matrix attached to a bilinear form or quadratic form on a finite-dimensional vector space: two matrices are congruent if and only if they represent the same bilinear form with respect to different bases.
Conjugate gradient, assuming exact arithmetic, converges in at most n steps, where n is the size of the matrix of the system (here n = 2). In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-semidefinite.
In particular, this is the case if the matrix A is independent of t. In the general case, however, the expression above is no longer the solution of the problem. The approach introduced by Magnus to solve the matrix initial-value problem is to express the solution by means of the exponential of a certain n × n matrix function Ω(t, t 0):
A formula editor is a computer program that is used to typeset mathematical formulas and mathematical expressions. Formula editors typically serve two purposes: They allow word processing and publication of technical content either for print publication, or to generate raster images for web pages or screen presentations.