To put the world of linear algebra to advanced use, it is not enough to
merely understand the theory; there is a significant gap between the
theory of linear algebra and its myriad expressions in nearly every
computational domain. To bridge this gap, it is essential to process the
theory by solving many exercises, thus obtaining a firmer grasp of its
diverse applications. Similarly, from a theoretical perspective, diving
into the literature on advanced linear algebra often reveals more and
more topics that are deferred to exercises instead of being treated in
the main text. As exercises grow more complex and numerous, it becomes
increasingly important to provide supporting material and guidelines on
how to solve them, supporting students' learning process.
This book provides precisely this type of supporting material for the
textbook "Numerical Linear Algebra and Matrix Factorizations," published
as Vol. 22 of Springer's Texts in Computational Science and
Engineering series. Instead of omitting details or merely providing
rough outlines, this book offers detailed proofs, and connects the
solutions to the corresponding results in the textbook. For the
algorithmic exercises the utmost level of detail is provided in the form
of MATLAB implementations. Both the textbook and solutions are
self-contained. This book and the textbook are of similar length,
demonstrating that solutions should not be considered a minor aspect
when learning at advanced levels.
