6.5-01 One orthogonalization step
One orthogonalization step One orthogonalization step removes the part of a vector already represented by earlier orthonormal directions. Practice follows the subtraction carefully, checks the remaining direction and handles normalization and nonunit basis vectors. What you will practise Subtract one or several orthogonal components. Calculate residuals and normalize them. Explain why the partial span is preserved. Handle already perpendicular and zero-residual cases. Begin with recognition and interpretation, then work through calculations, error diagnosis and more demanding reasoning. Single-select and multi-select questions ask you to evaluate the stated assumptions as well as the result. Worked explanations connect the answer to a method or a counterexample, so you can check why tempting alternatives fail. Before you start Review orthogonal projection and normalization. Keep a written calculation or short justification for each response, especially when several statements can be correct. This microlearning supports the complete Gram–Schmidt algorithm within Module 6 of the Complete Linear Algebra Course.
Oct 20, 2026
