In visualizing the mathematical concepts, some are inherently more dynamic in nature than others. For instance, the algorithmic ones such as Gram-Schmidt process has this idiosyncrasy. Often the complexity of the mathematical expression, independent of conceptual complexity, tends to invoke the anxiety within the learner at an early learning stage. Even the one that is readily perceived as natural and intuitive often involves a complex mathematical expression for its description. In order to minimize the mathematical anxiety provoked at an eyeball observation, the animation method can be the most effective remedy in the instructional design.
One feature to note in using the following application is that while mathematical concept is being explained visually, the corresponding Mathematica command pops up in response to a mouseover action on the specific part of the animation clip.