Development of a mathematical Graphical User Interface (GUI) face recognition application using MATLAB® platform. Linear algebra was used to construct the integrated model for: error detection, graphical user interface, computer vision, pattern recognition, digital image processing, artificial intelligence, as well as Google's page rank algorithm. The application was validated using 400 image set; 200 images for testing, and 200 for training, and resulted in recognition accuracy of 96.75% for both images and videos. The recognition timing was further improved by the introduction of Principal Component Analysis (PCA) Eigenfaces algorithm on frames of the key.