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2. Linear relation - Wikipedia

   en.wikipedia.org/wiki/Linear_relation

   In linear algebra, a linear relation, or simply relation, between elements of a vector space or a module is a linear equation that has these elements as a solution.. More precisely, if , …, are elements of a (left) module M over a ring R (the case of a vector space over a field is a special case), a relation between , …, is a sequence (, …,) of elements of R such that

3. Linear recurrence with constant coefficients - Wikipedia

   en.wikipedia.org/wiki/Linear_recurrence_with...

   In mathematics (including combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients [1]: ch. 17 [2]: ch. 10 (also known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial that is linear in the various iterates of a variable—that is, in the values of the elements of a sequence.

4. Linearity - Wikipedia

   en.wikipedia.org/wiki/Linearity

   In mathematics, the term linear is used in two distinct senses for two different properties: . linearity of a function (or mapping);; linearity of a polynomial.; An example of a linear function is the function defined by () = (,) that maps the real line to a line in the Euclidean plane R 2 that passes through the origin.

5. Householder transformation - Wikipedia

   en.wikipedia.org/wiki/Householder_transformation

   Householder transformations are widely used in numerical linear algebra, for example, to annihilate the entries below the main diagonal of a matrix, [2] to perform QR decompositions and in the first step of the QR algorithm. They are also widely used for transforming to a Hessenberg form.

6. Linear algebra - Wikipedia

   en.wikipedia.org/wiki/Linear_algebra

   Linear algebra is the branch of ... is a typical example of a real ... a video presentation from 3Blue1Brown of the basics of linear algebra, with emphasis on the ...

7. Linear dynamical system - Wikipedia

   en.wikipedia.org/wiki/Linear_dynamical_system

   Linear dynamical systems can be solved exactly, in contrast to most nonlinear ones. Occasionally, a nonlinear system can be solved exactly by a change of variables to a linear system. Moreover, the solutions of (almost) any nonlinear system can be well-approximated by an equivalent linear system near its fixed points. Hence, understanding ...

8. Linear programming - Wikipedia

   en.wikipedia.org/wiki/Linear_programming

   Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).

9. Functional analysis - Wikipedia

   en.wikipedia.org/wiki/Functional_analysis

   Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, inner product, norm, or topology) and the linear functions defined on these spaces and suitably respecting these structures.