Characteristic Vector (other)
A characteristic vector may refer to: * an eigenvector * an indicator vector In mathematics, the indicator vector or characteristic vector or incidence vector of a subset ''T'' of a Set (mathematics), set ''S'' is the vector x_T := (x_s)_ such that x_s = 1 if s \in T and x_s = 0 if s \notin T. If ''S'' is countable set, cou ...

Eigenvalues And Eigenvectors
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 ...
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