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Any short exact sequence of vector spaces is split exact. This is a rephrasing of the fact that any set of linearly independent vectors in a vector space can be extended to a basis . The exact sequence 0 → Z → 2 Z → Z / 2 Z → 0 {\displaystyle 0\to \mathbf {Z} \mathrel {\stackrel {2}{\to }} \mathbf {Z} \to \mathbf {Z} /2\mathbf {Z} \to 0 ...
In the mathematical discipline of numerical linear algebra, a matrix splitting is an expression which represents a given matrix as a sum or difference of matrices. Many iterative methods (for example, for systems of differential equations) depend upon the direct solution of matrix equations involving matrices more general than tridiagonal matrices.
Splitting, also called binary thinking, dichotomous thinking, black-and-white thinking, all-or-nothing thinking, or thinking in extremes, is the failure in a person's thinking to bring together the dichotomy of both perceived positive and negative qualities of something into a cohesive, realistic whole.
Projection method (fluid dynamics) — computational fluid dynamics method; Reactive transport modeling in porous media — modeling of chemical reactions and fluid flow through the Earth's crust; Richard S. Varga — developed matrix splitting; Strang splitting — specific numerical method for solving differential equations using operator ...
In mathematics, binary splitting is a technique for speeding up numerical evaluation of many types of series with rational terms. In particular, it can be used to evaluate hypergeometric series at rational points.
The method is based on finite differences where the differentiation operators exhibit summation-by-parts properties. Typically, these operators consist of differentiation matrices with central difference stencils in the interior with carefully chosen one-sided boundary stencils designed to mimic integration-by-parts in the discrete setting.
The Sioux Falls School District Board of Education heard three options from district officials again about the future of Whittier Middle School before it will vote on those options June 10.
For a direct sum this is clear, as one can inject from or project to the summands. For a left split sequence, the map t × r: B → A × C gives an isomorphism, so B is a direct sum (3.), and thus inverting the isomorphism and composing with the natural injection C → A × C gives an injection C → B splitting r (2.).