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Johnson Scheme
In mathematics, the Johnson scheme, named after Selmer M. Johnson, is also known as the triangular association scheme. It consists of the set of all binary vectors ''X'' of length ''ℓ'' and weight ''n'', such that v=\left, X\=\binom.F. J. MacWilliams and N. J. A. Sloane, ''The Theory of Error-Correcting Codes'', Elsevier, New York, 1978. Two vectors ''x'', ''y'' ∈ ''X'' are called ''i''th associates if dist(''x'', ''y'') = 2''i'' for ''i'' = 0, 1, ..., ''n''. The eigenvalues In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted b ... are given by : p_\left(k\right)=E_\left(k\right), : q_\left(i\right)=\fracE_\left(k\right), where : \mu_=\frac\binom, and ''E''''k''(''x'') is an Eberlein polynomial defined by : E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Selmer M
Selmer may refer to: * Selmer (surname) * Selmer (given name) * Selmer, Tennessee, United States, a town * Selmer group, a group constructed from an isogeny of abelian varieties See also * Conn-Selmer, a manufacturer and distributor of musical instruments * Henri Selmer Paris Henri Selmer Paris is a French enterprise, manufacturer of musical instruments based at Mantes-la-Ville near Paris. Founded in 1885, it is known as a producer of professional-grade woodwind and brass instruments, especially saxophones, clarinet ..., a musical instrument manufacturer, associated with Conn-Selmer * Semler, a surname {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Association Scheme
The theory of association schemes arose in statistics, in the theory of experimental design for the analysis of variance. In mathematics, association schemes belong to both algebra and combinatorics. In algebraic combinatorics, association schemes provide a unified approach to many topics, for example combinatorial designs and coding theory. In algebra, association schemes generalize groups, and the theory of association schemes generalizes the character theory of linear representations of groups. Definition An ''n''-class association scheme consists of a set ''X'' together with a partition ''S'' of ''X'' × ''X'' into ''n'' + 1 binary relations, ''R''0, ''R''1, ..., ''R''''n'' which satisfy: *R_ = \ and is called the identity relation. *Defining R^* := \, if ''R'' in ''S'', then ''R*'' in ''S'' *If (x,y) \in R_, the number of z \in X such that (x,z) \in R_ and (z,y) \in R_ is a constant p^k_ depending on i, j, k but not on the particular choice of x and y. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenvalues
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by \lambda, is the factor by which the eigenvector is scaled. Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated. Formal definition If is a linear transformation from a vector space over a field into itself and is a nonzero vector in , then is an eigenvector of if is a scalar multiple of . This can be written as T(\mathbf) = \lambda \mathbf, where is a scalar in , known as the eigenvalue, characteristic value, or characteristic root ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
