eigenvalue

English - Turkish

Definition of eigenvalue in English Turkish dictionary

(Nükleer Bilimler) özgün değer

gizdeğer

özdeğer

Bir denklemin şartlarından birinin müsait olabilen değerlerinden biri

öz değer

Related Terms

eigenvalue equation

ozdeger denklemi

English - English

Definition of eigenvalue in English English dictionary

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

Related Terms

eigenvalues

plural of eigenvalue

Hyphenation

ei·gen·val·ue

Synonyms

characteristic root, characteristic value, eigenroot, latent value

Etymology

() eigen- +‎ value