In the present thesis, there carried out the study of the mathematical technique of the Analysis of Principal Components – PCA. It was used for the persons' facial recognition and gotten to decrease the rate of mistake. To get this aim, it used images that were taken of the base faces of the Olivetti Research Laboratory, which have low resolution and are in grayscale._x000D_ With the purpose of achieving better results in the recognition, the first step that was realized is to apply a series of Gabor's Filters, in different frequencies and orientations, searching with this to highlight the most relevant characteristics of the face in the images._x000D_ On these images obtained of Gabor's Filter, the second step was realized with the application of the technique of the Analysis of Principal Components - PCA, the purpose of decreasing the dimension of the set of patterns that they repres...