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2. Linear algebra - Wikipedia

   en.wikipedia.org/wiki/Linear_algebra

   The application of linear algebra in this context is vital for the design and operation of modern power systems, including renewable energy sources and smart grids. Overall, the application of linear algebra in fluid mechanics, fluid dynamics, and thermal energy systems is an example of the profound interconnection between mathematics and ...

3. LU decomposition - Wikipedia

   en.wikipedia.org/wiki/LU_decomposition

   The solution of N linear equations in N unknowns by elimination was already known to ancient Chinese. [20] Subsequently, many mathematicians were performing and perfecting it yet as the method became relegated to school grade, few of them left any detailed descriptions.

4. Weak formulation - Wikipedia

   en.wikipedia.org/wiki/Weak_formulation

   Let be a Banach space, let ′ be the dual space of , let : ′ be a linear map, and let ′.A vector is a solution of the equation = if and only if for all , () = ().A particular choice of is called a test vector (in general) or a test function (if is a function space).

5. Outline of linear algebra - Wikipedia

   en.wikipedia.org/wiki/Outline_of_linear_algebra

   This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector ...

6. Linear complementarity problem - Wikipedia

   en.wikipedia.org/wiki/Linear_complementarity_problem

   In mathematical optimization theory, the linear complementarity problem (LCP) arises frequently in computational mechanics and encompasses the well-known quadratic programming as a special case. It was proposed by Cottle and Dantzig in 1968.

7. System of linear equations - Wikipedia

   en.wikipedia.org/wiki/System_of_linear_equations

   Because a solution to a linear system must satisfy all of the equations, the solution set is the intersection of these lines, and is hence either a line, a single point, or the empty set. For three variables, each linear equation determines a plane in three-dimensional space , and the solution set is the intersection of these planes.

8. Cramer's rule - Wikipedia

   en.wikipedia.org/wiki/Cramer's_rule

   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 ...

9. Linear Algebra and Its Applications - Wikipedia

   en.wikipedia.org/wiki/Linear_Algebra_and_Its...

   Linear Algebra and its Applications is a biweekly peer-reviewed mathematics journal published by Elsevier and covering matrix theory and finite-dimensional linear ...