The aim of this article is to share with the educational and scientific community, the usefulness of the new program called Matrix Calculator. That program has been used since the academic year 2011-2012, mainly in teaching Linear Algebra, in the first year of the different degrees of Tecnun, School of Engineering. (University of Navarra, in San Sebastian, Spain). It has been found that meets all expectations for student learning, while providing a great attraction for the study of Linear Algebra, mainly in its practical side. The application has been developed using MATLAB (R). The Matrix Calculator consists of a separate set of more than 150 functions. These functions and the main program are accompanied by a simple pdf file with the user's instructions and a set of solved examples.

This article presents nine different methods of orthogonal projection onto a hyperspace defined by points. These methods have been implemented in MATLAB language. Comparisons have been made of numerical precision and cpu times, taking one of them as a reference. It has placed special emphasis on an inversion's method with comments to its potential and some demonstrations that justify the intermediate steps used.