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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. System of linear equations - Wikipedia

   en.wikipedia.org/wiki/System_of_linear_equations

   A solution of a linear system is an assignment of values to the variables ,, …, such that each of the equations is satisfied. The set of all possible solutions is called the solution set. [5] A linear system may behave in any one of three possible ways: The system has infinitely many solutions.

4. LU decomposition - Wikipedia

   en.wikipedia.org/wiki/LU_decomposition

   The solution of N linear equations in N unknowns by ... public class ... Steven R.; McDonald, Judi J. (2021), Linear Algebra and its Applications (Sixth ...

5. 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 algebra. History [ edit ]

6. Numerical linear algebra - Wikipedia

   en.wikipedia.org/wiki/Numerical_linear_algebra

   Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra.

7. Moore–Penrose inverse - Wikipedia

   en.wikipedia.org/wiki/Moore–Penrose_inverse

   A common use of the pseudoinverse is to compute a "best fit" (least squares) approximate solution to a system of linear equations that lacks an exact solution (see below under § Applications). Another use is to find the minimum norm solution to a system of linear equations with multiple solutions. The pseudoinverse facilitates the statement ...

8. Symmetric matrix - Wikipedia

   en.wikipedia.org/wiki/Symmetric_matrix

   In linear algebra, a real symmetric matrix represents a self-adjoint operator [1] represented in an orthonormal basis over a real inner product space. The corresponding object for a complex inner product space is a Hermitian matrix with complex-valued entries, which is equal to its conjugate transpose .

9. Permanent (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Permanent_(mathematics)

   Let Ω(n,k) be the class of all (0, 1)-matrices of order n with each row and column sum equal to k. Every matrix A in this class has perm(A) > 0. [13] The incidence matrices of projective planes are in the class Ω(n 2 + n + 1, n + 1) for n an integer > 1. The permanents corresponding to the smallest projective planes have been calculated.