system of linear equations

  • 1System of linear equations — In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables. For example,:egin{alignat}{7}3x ; + ; 2y ; ; z ; = ; 1 2x ; ; 2y ; + ; 4z ; = ; 2 x ; + ; frac{1}{2} y ; ; z …

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  • 2Linear least squares — is an important computational problem, that arises primarily in applications when it is desired to fit a linear mathematical model to measurements obtained from experiments. The goals of linear least squares are to extract predictions from the… …

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  • 3Linear least squares (mathematics) — This article is about the mathematics that underlie curve fitting using linear least squares. For statistical regression analysis using least squares, see linear regression. For linear regression on a single variable, see simple linear regression …

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  • 4Linear algebra — R3 is a vector (linear) space, and lines and planes passing through the origin are vector subspaces in R3. Subspaces are a common object of study in linear algebra. Linear algebra is a branch of mathematics that studies vector spaces, also called …

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  • 5Linear system — A linear system is a mathematical model of a system based on the use of a linear operator.Linear systems typically exhibit features and properties that are much simpler than the general, nonlinear case.As a mathematical abstraction or… …

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  • 6Linear combination — In mathematics, linear combinations are a concept central to linear algebra and related fields of mathematics.Most of this article deals with linear combinations in the context of a vector space over a field, with some generalisations given at… …

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  • 7system of equations — or simultaneous equations In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns …

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  • 8Linear least squares/Proposed — Linear least squares is an important computational problem, that arises primarily in applications when it is desired to fit a linear mathematical model to observations obtained from experiments. Mathematically, it can be stated as the problem of… …

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  • 9Linear programming — (LP, or linear optimization) is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear relationships.… …

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  • 10Linear elasticity — Continuum mechanics …

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  • 11Linear regression — Example of simple linear regression, which has one independent variable In statistics, linear regression is an approach to modeling the relationship between a scalar variable y and one or more explanatory variables denoted X. The case of one… …

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  • 12linear equation — Math. 1. a first order equation involving two variables: its graph is a straight line in the Cartesian coordinate system. 2. any equation such that the sum of two solutions is a solution, and a constant multiple of a solution is a solution. Cf.… …

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  • 13linear algebra — Math. See under algebra (def. 2). [1890 95] * * * Branch of algebra concerned with methods of solving systems of linear equations; more generally, the mathematics of linear transformations and vector spaces. Linear refers to the form of the… …

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  • 14Linear — The word linear comes from the Latin word linearis , which means created by lines .In advanced mathematics, a linear map or function f ( x ) is a function which satisfies the following two properties:* Additivity (also called the superposition… …

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  • 15linear programming — Math. any of several methods for finding where a given linear function of several nonnegative variables assumes an extreme value and for determining the extreme value, the variable usually being subjected to constraints in the form of linear… …

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  • 16Linear congruence theorem — In modular arithmetic, the question of when a linear congruence can be solved is answered by the linear congruence theorem. If a and b are any integers and n is a positive integer, then the congruence: ax equiv; b (mod n ) (1)has a solution for x …

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  • 17Linear prediction — is a mathematical operation where future values of a discrete time signal are estimated as a linear function of previous samples.In digital signal processing, linear prediction is often called linear predictive coding (LPC) and can thus be viewed …

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  • 18System of Physical Quantities — of Nikolay A. Plotnikov (SPQ) the classification of physical quantities or physical operators, that makes it possible to reveal their dependence on the geometry of space time and fundamental physical constants in the form of differential… …

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  • 19Linear-quadratic-Gaussian control — In control theory, the linear quadratic Gaussian (LQG) control problem is one of the most fundamental optimal control problems. It concerns uncertain linear systems disturbed by additive white Gaussian noise, having incomplete state information… …

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  • 20Linear system of divisors — A linear system of divisors algebraicizes the classic geometric notion of a family of curves, as in the Apollonian circles. In algebraic geometry, a linear system of divisors is an algebraic generalization of the geometric notion of a family of… …

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