*8.2.1
Rotation of configuration*

#### Rotation
with principal axes

The configuration is rotated so that successive dimensions account for the
maximum possible variance. The symmetric matrix *A*^{T}A of
dimensions (*p **´ p*) is
computed and eigenvectors *P* of *A*^{T}A are
determined, using Jacobi’s diagonalization method.

The matrix *A* is transformed into a matrix *B* of *b*_{is}
elements, such that *B* = *AP*_{p}, *B*
having *n* rows and *p* columns like the matrix *A.*

#### Rotated Configuration

The rotation can be performed only on two dimensions at a time. It is up to
the researcher to select the dimensions and the angle f of rotation.

*a*_{il} =

The calculations are performed for each value of *i* (variable) and as
many times as there are variables.

#### Varimax rotation

The elements *a*_{is} of *A* are normalized by the
square roots of the communalities corresponding to each variable. Define

Having constructed *B* =, find the best projection axes for
the variables, after equalization of their inertia. Define the function

The maximization of the function *V*_{e} is performed through
successive rotations of two dimensions at a time, until convergence is reached.

The resulting matrix *B* of *b*_{i}_{s}
elements has the same number of rows and columns as the initial matrix *A.*

The module Config also
computes the matrices of Scalar products and Inter-point distances. These
metrics are computed by the following formulae:

*Matrix of Inter-point distances*:

This is a square and symmetric matrices of Euclidean distances between
variables.

*Matrix of scalar products *

The matrix *SP* is a square and symmetric matrix of scalar
products of variables. If each variable is centered and normalized (mean = 0,
standard deviation = 1), then the matrix *SP* becomes a correlation
matrix.