I have the definition of a mathematical model in English and I have translated it, but I do not think it is correct, I can not figure it out how to translate a little part of it... Can you please suggest a better translation or just give a comment about the translation?
Original:
PCA is a mathematical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. The number of principal components is less than or equal to the number of original variables. This transformation is defined in such a way that the first principal component has the largest possible variance (that is, accounts for as much of the variability in the data as possible), and each succeeding component in turn has the highest variance possible under the constraint that it be orthogonal to (i.e., uncorrelated with) the preceding components. Principal components are guaranteed to be independent only if the data set is jointly normally distributed. PCA is sensitive to the relative scaling of the original variables.
Translated version:
PCA es un procedimiento matemático que utiliza una transformación ortogonal para convertir un conjunto de observaciones de variables posiblemente correlacionadas en un conjunto de valores de variables linealmente no correlacionadas denominados componentes principales. El número de componentes principales es menor o igual al número de variables originales. Esta transformación se define de tal manera que el primer componente principal tiene la varianza más grande posible (...), su vez cada componente subsiguiente tiene la mayor varianza posible cumpliendo la condición de que sean ortogonales (es decir, que no esten correlacionadas ) a los componentes anteriores. Los componentes principales serán independientes sólo si el conjunto de datos esta uniformemente distribuido. ...