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With respect to general linear maps, linear endomorphisms and square matrices have some specific properties that make their study an important part of linear algebra, which is used in many parts of mathematics, including geometric transformations, coordinate changes, quadratic forms, and many other part of mathematics.
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 spaces and through matrices. Linear equations
The basic operation of linear interpolation between two values is commonly used in computer graphics. In that field's jargon it is sometimes called a lerp (from l inear int erp olation). The term can be used as a verb or noun for the operation. e.g. " Bresenham's algorithm lerps incrementally between the two endpoints of the line."
For example, the collection of all possible linear combinations of the vectors on the left-hand side (LHS) is called their span, and the equations have a solution just when the right-hand vector is within that span. If every vector within that span has exactly one expression as a linear combination of the given left-hand vectors, then any ...
In linear programming, a discipline within applied mathematics, a basic solution is any solution of a linear programming problem satisfying certain specified technical conditions. For a polyhedron P {\displaystyle P} and a vector x ∗ ∈ R n {\displaystyle \mathbf {x} ^{*}\in \mathbb {R} ^{n}} , x ∗ {\displaystyle \mathbf {x} ^{*}} is a ...
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).
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