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In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems.
The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations .
[11] [12] For factual question answering, WolframAlpha was used by Apple's Siri in October 2011 and Amazon Alexa in December 2018 for math and science queries. [13] [14] Users would notice that the Wolfram Integration for Siri was changed in June 2013 to use Bing to query certain results on IOS 7. [15]
Wolfram Language which is used within many Wolfram technologies such as Mathematica and the Wolfram Cloud; World Programming System (WPS), supports mixing Python, R and SAS languages in a single-user program for statistical analysis and data manipulation; Yorick is an interpreted programming language designed for numerics, graph plotting and ...
Mathematical chemistry [1] is the area of research engaged in novel applications of mathematics to chemistry; it concerns itself principally with the mathematical modeling of chemical phenomena. [2] Mathematical chemistry has also sometimes been called computer chemistry , but should not be confused with computational chemistry .
The following tables provide a comparison of computer algebra systems (CAS). [ 1 ] [ 2 ] [ 3 ] A CAS is a package comprising a set of algorithms for performing symbolic manipulations on algebraic objects, a language to implement them, and an environment in which to use the language.
A chemical equation is the symbolic representation of a chemical reaction in the form of symbols and chemical formulas.The reactant entities are given on the left-hand side and the product entities are on the right-hand side with a plus sign between the entities in both the reactants and the products, and an arrow that points towards the products to show the direction of the reaction. [1]
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one column by the ...