Linear Algebra and the C Language/a0pe

__NOTOC__ Projection of the space onto a hyperplan: The matrix A projects the hyperspace in the direction of the eigenvector V4 on a hyperplan determined by the eigenvector V1, V2, and V3 if : * The eigenvector V1 has its eigenvalue equal to one and * The eigenvector V2 has its eigenvalue equal to one and * The eigenvector V3 has its eigenvalue equal to one and * The eigenvector V4 has its eigenvalue equal to zero and * If The vectors V1, V2, V3 and V4 are linearly independent In these examples, you choose the vectors of the hyperplan and the vector for the projection. You compute the matrix A that projects the hyperspace in the direction of the eigenvector V4 onto an hyperplan determined by the eigenvectors V1, V2, V3. Next, you can calculate the projection of a point P onto the hyperplan. The application You can choose the vectors of the hyperplan and the vector for the projection. c00a.c You create the matrix A. c00b.c You verify the properties of the matrix A. c00c.c You can calculate the projection of a point P onto the hyperplan. c00d.c Check if the projection of a point P lies on the hyperplan. c00e.c