Linear Algebra Advanced Course

In linear algebra we work with the language we use when many conditions that involve many variables must be satisfied simultaneously. The conditions might achieve different forms as they are expressed in different coordinates, and we might need to introduce suitable coordinates or refine them. An objective in this work is often to separate the conditions that appear from each other. In no complete separation can be achieved, then we usually try to simplify the dependencies that appear between the resulting conditions as far as possible. In science and technology, a precision that usually widely supersedes the objectives in social sciences is aimed at. Hunting precision usually implies different optimization problems. In these problems, different special cases may arise. One of the problems might be that complete separation is not possible. Today we have possibilities to collect and store significantly larger amounts of data than the amounts we had possibilities to deal with just a few decades ago and this requires efficient methods for the analysis these data sets. The course ends up with the singular value decomposition that constitutes the crown of work of many of the methods that have been introduced during the course and simultaneously provides far-reaching application in image processing and statistical data analysis.