Recap: what is the Eigenvalue?

The Eigenvalue is a numerical value that describes the amount by which a linear transformation changes the size of a vector. It is calculated by taking the determinant of a matrix associated with the linear transformation. In general, if the linear transformation is larger, then the Eigenvalue will also be larger. The eigenvalues of a matrix tell us about the linear transformations behavior such as its change in size, direction, and the nature of the transformation.

- Share of the variance of all variables that is included in one factor. - If a factor contains exactly one variable, its eigenvalue equals 1. Thus, a composed factor should also achieve at least this value (= Kaiser criterion). - because otherwise the factor has less explanatory value than the single variable - Eigenvalue of a factor equals the sum of squared factor loadings of this factor over all variables - Eigenvalue (factorm) = sum (j=1->n) of a(jm)²