Loading...
3 results
Search Results
Now showing 1 - 3 of 3
- Block eigenvectors obtained by block hotelling deflationPublication . M. L. Martins, Fernando; Pereira, Edgar; Vitória, JoséThe computation of block eigenvalues and block eigenvectors of a matrix partitioned into blocks is dealt with. A block version of a Hotelling deflation process and a block spectral decomposition are presented.
- Geometric illustrations of the conjugacy principlePublication . M. L. Martins, Fernando; Vicente, M. A. FacasIn this paper, we illustrate the use of the conjugacy principle in several geometric transformations: translations, reflections and rotations. Our context are the real spaces R2 and R3. The main role is played by matrices, as it is to be expected. The referred to transformations are fundamental when studying motion questions in the Mechanics, Computer Graphics, Robotics, Computer Games, etc.. Our didactical goals are focused on the acquisition and development of spatial abilities, in order to get a better perception, interpretation and forecasting of the geometrical transformations in our physical world.
- Conjugacy and geometry I : foot of the perpendicular, distance and gram determinantPublication . Costa, Cecília; Martins, Fernando M. L.; Serôdio, Rogério; Tadeu, Pedro; Vincente, M. A. Facas; Vitória, JoséIn this note on space geometry, the Gram determinant is used for expressing distances, vectors whose magnitude equals those distances and best approximation points. Three cases are considered: distances from a point to a line and to a plane and distances between two skew lines. (Symbolic) determinants occur in the expressions of the feet of perpendiculars and in the representation of the vectors materializing the distances. Because best approximation problems often require the use of subspaces, in order to solve the general cases of the proposed problems, we make extensive use of the conjugacy principle much present in Mathematics. The main purpose of this paper, focused on the resolution of distance problems in tridimensional geometry, is to provide the acquisition of spatial abilities through the proposed constructive approach. The obtained results, which could be a starting point and give clues for solving more advanced geometry problems, are applicable in several fields of practical sciences, such as the Coordinate Metrology, for instance. Moreover, this paper may be a window for coming across with a diversity of scalar products.