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Glite Dictionary
eigenvalue

eigenvalue

2 9.9
A number for a square matrix that makes some nonzero vector bigger or smaller when multiplied by the matrix
  • noun
  • /ˈaɪɡənˌvælju/
  • Specialized
translation icon : valor propio
  • In linear algebra, an eigenvalue represents a scalar that scales a corresponding eigenvector when a transformation is applied.
  • factors and eigenvalues
  • eigenvalues and eigenvectors
  • minimum eigenvalue

Examples

  • The Kaiser criterion recommends that all factors with eigenvalues greater than one be considered.

    Academic text (2008)

  • The PCA showed that the first factor with an eigenvalue of 4.68 accounted for 78% of the variance.

    Academic text (2013)

  • This would have an eigenvalue smaller than that.

  • However, in each case, every factor had an eigenvalue of 1.0 or larger.

    Academic text (1996)

  • None of the factors after the first one had eigenvalues greater than one.

    Academic text (1996)

  • The initial factor extraction, using eigenvalue = 1.0 as criteria, resulted in a 10-factor model.

    Academic text (1992)

  • In practice, we can leave out insignificant eigenvalues and still get reasonably good results.

    Academic text (2017)

  • The significant loadings on the two factors, eigenvalues, and percentage of variance are reported in Table 1.

    Academic text (1996)

  • For the compensatory consumption scale, EFA revealed three factors with Eigenvalues greater than 1.0.

    Academic text (2008)

  • The analysis yielded three factors with eigenvalues higher than 1.0, which explained 53.27% of the variance.

    Academic text (2008)

Synonyms

characteristic root
vseigenvalue
  • Specialized
9.9

A number that makes a square matrix have determinant zero when subtracted from its diagonal entries

is the same mathematical concept but expressed with an alternate name

Surface Forms

eigenvalue singular
eigenvalues plural

Morphology

eigenvalue = eigen + value (opaque) = eigen + value

The combining form 'eigen-' is a technical borrowing not productive in general English, so knowing 'value' alone does not allow a learner to infer the mathematical sense.

Etymology

Eigenvalue comes from the German part eigen, which means 'own' or 'characteristic', plus value, meaning 'number'. So an eigenvalue is a special number that 'belongs' to a matrix and shows an important feature of that matrix.