Search results
Results From The WOW.Com Content Network
The linear dependency of a sequence of vectors does not depend of the order of the terms in the sequence. This allows defining linear independence for a finite set of vectors: A finite set of vectors is linearly independent if the sequence obtained by ordering them is linearly independent. In other words, one has the following result that is ...
In combinatorics, a matroid / ˈ m eɪ t r ɔɪ d / is a structure that abstracts and generalizes the notion of linear independence in vector spaces.There are many equivalent ways to define a matroid axiomatically, the most significant being in terms of: independent sets; bases or circuits; rank functions; closure operators; and closed sets or flats.
In the mathematical theory of matroids, a matroid representation is a family of vectors whose linear independence relation is the same as that of a given matroid. Matroid representations are analogous to group representations; both types of representation provide abstract algebraic structures (matroids and groups respectively) with concrete descriptions in terms of linear algebra.
The theorem is also known variously as the Hermite–Lindemann theorem and the Hermite–Lindemann–Weierstrass theorem.Charles Hermite first proved the simpler theorem where the α i exponents are required to be rational integers and linear independence is only assured over the rational integers, [4] [5] a result sometimes referred to as Hermite's theorem. [6]
The Great Warrior Skanderbeg (Albanian: Luftëtari i madh i Shqipërisë Skënderbeu; Russian: Великий воин Албании Скандербег, romanized: Velikiy voin Albanii Skanderbeg) is a 1953 Soviet-Albanian biopic directed by Sergei Yutkevich.
From Wikipedia, the free encyclopedia. Redirect page
is the linear combination of vectors and such that = +. In mathematics, a linear combination or superposition is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).
It should at least be mentioned that in a module over a ring, linear independence (in the sense that zero cannot be represented as a non-trivial linear combination) is not equivalent to one vector being contained in the span of the remaining elements.--80.136.131.201 18:37, 20 January 2006 (UTC)