eigenvalue

Английский Язык - Турецкий язык

Определение eigenvalue в Английский Язык Турецкий язык словарь: (Nükleer Bilimler) özgün değer; gizdeğer; özdeğer; Bir denklemin şartlarından birinin müsait olabilen değerlerinden biri; öz değer
eigenvalue equation: ozdeger denklemi

Английский Язык - Английский Язык

Определение eigenvalue в Английский Язык Английский Язык словарь: The change in magnitude of a vector that does not change in direction under a given linear transformation; a scalar factor by which an eigenvector is multiplied under such a transformation
The eigenvalues \lambda\! of a transformation matrix \rm M\! may be found by solving \det({\rm M} - \lambda {\rm I}) = 0\! .; (Mathematics & Physics) a value of a parameter for which a differential equation has a non-zero solution (an eigenfunction) under given conditions; the proportion of the total between-group separation that is contributed by each discriminant function; of a matrix: An eigenvalue of a square matrix A is a scalar c such that Ax = cx holds for some nonzero vector x See also: eigenvector ON p399; Str S6 1; AR7 p355; of a matrix: An eigenvalue of a n by n matrix A is a scalar c such that A*x = c*x holds for some nonzero vector x (where x is an n-tuple) See also: eigenvector; the variance in a set of variables explained by a factor or component, and denoted by lambda An eigenvalue is the sum of squared values in the column of a factor matrix, or where aik is the factor loading for variable i on factor k, and m is the number of variables In matrix algebra the principal eigenvalues of a correlation matrix R are the roots of the characteristic equation; the length of a principal component which measures the variance of a principal component band See also principal components; The amount a particular eigenvector is scaled when transformed; of a matrix: An eigenvalue of a square matrix A is a scalar c such that Ax = cx holds for some nonzero vector x See also: eigenvector; and eigenvector 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; In mathematical analysis, one of a set of discrete values of a parameter, k, in an equation of the form Lx = kx. Such characteristic equations are particularly useful in solving differential equations, integral equations, and systems of equations. In the equation, L is a linear transformation such as a matrix or a differential operator, and x can be a vector or a function (called an eigenvector or eigenfunction). The totality of eigenvalues for a given characteristic equation is a set. In quantum mechanics, where L is an energy operator, the eigenvalues are energy values; {i} characteristic root, proper value, latent root (Mathematics); The change in magnitude of a vector that is not rotated under a given linear transformation; formally, a scalar lambda such that, for a particular matrix A, A x = lambda x for some nonzero vector x, an eigenvector of the matrix; thus, a value of lambda such that mathrm{det}(A - lambda I) = 0 for a given square matrix A, where I is the identity matrix and mathrm{det} is the determinant operator
eigenvalues: plural of eigenvalue