Orthogonalization algorithm

The orthogonalization algorithm

In this lesson we present the orthogonalization algorithm with which all the algebra problems that are going to be solved will be solved. The algorithm receives this name, since it obtains the subspace orthogonal to a given subspace and its complementary subspace. To do this, the algorithm with examples is described step by step.

Orthogonal subspaces and complements

In this lesson it is shown how the orthogonalization algorithm can be used to obtain the orthogonal subspace of a linear subspace. The properties of theis algorithm are incredible, as it is shown.

Elemental transformations of matrices

In this lesson we explain how to transform matrices using post and pre multiplication by matrices, which produce column and row transformations, respectively. Three types of matrices are defined, which come from the identity matrix replacing one diagonal element, a non-diagonal element or permuting two rows or columns. These matrices are used to produce the same transformations as the algorithm in the different iterations. They are used to demonstrate the formula for the determinant of a matrix.