If a (scalar) value, t, satisfies Ax = tx for some vector, x not= 0, it is an eigenvalue of the matrix A, and x is an eigenvector. In mathematical programming this arises in the context of convergence analysis, where A is the hessian of some merit function, such as the objective or Lagrangian.
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http://glossary.computing.society.informs.org/index.php?page=E.html
(from the article `algebra, linear`) When studying linear transformations, it is extremely useful to find nonzero vectors whose direction is left unchanged by the transformation. These ...
Found on
http://www.britannica.com/eb/a-z/e/14
For each eigenvalue L of a square matrix A there is an associated right eigenvector, denoted b that has the dimension of the number of rows of A. The right eigenvector satisfies: Ab = Lb Contexts: linear algebra
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http://www.econterms.com/glossary.cgi?query=eigenvector
A unit length vector that retains its direction when multiplied to the matrix that it corresponds to. An (n * n) matrix can have as many as n unique eigenvectors, each of which will have its own eigenvalue.
Found on
http://www.encyclo.co.uk/local/20090
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