Linear Algebra. (Q5907011)

[See the review of the first edition (1979; Zbl 0409.15002).] This is, within the last twenty-five years, the tenth edition of one of the most popular German introductory textbooks of undergraduate linear algebra. Grown out of a basic course taught back in 1970/1971 at the University of Regensburg for freshmen in mathematics and physics, simultaneously, the text has maintained both its peculiar charm and its attractivity for beginners, over all these decades. This is because it is really a course book, or a class-room text, focusing on lively teaching the very basics instead of presenting an accumulation of more than digestible material for freshmen. The text covers, in eleven chapters, just the very basics of linear algebra (sets, vector spaces, bases and dimension, linear maps and matrices, determinants, systems of linear equations, inner product spaces and orthogonality, eigenvalues, self-adjoint operators and the spectral theorem, Sylvester's law of inertia, and the Jordan classification of matrices), without going very much into abstract depth, but it comforts the beginner in the field by its passionate didactic devotion, empathy, vividness, and motivating power. As in the earlier editions of his book, the author has set a high value on optical aesthetics and lucidity, too, and in this tenth edition he has even topped this peculiarity. Otherwise left intact, apart from a few minor improvements with regard to the contents, the text has been given a completely new, modern layout. For the sake of lucidity, the main parts of the text appear now in a framing, which will help the reader to distinguish between the essentials and the explaining side remarks. The particular features of the text, above all the many beautiful, illustrating pictures, the markings for students of mathematics or physics, respectively, and the non-standard design of the exercises and quizzes have been kept, of course. All together, this elementary standard text of linear algebra serves its purpose, now as before, and this tenth edition will surely not be the last one. This is because this well-proved classic is and remains just ideal for the very beginners, especially for students of physics, mathematical didactics, other natural sciences, and engineering. In regard of this very fact, it appears quite strange that this lovely primer has never been translated for a wider, international public.