| dc.description.abstract | This book originates from a collection of lecture notes that the first author prepared
at the University of Trieste with Michela Brundu, over a span of fifteen years,
together with the more recent one written by the second author. The notes were
meant for undergraduate classes on linear algebra, geometry and more generally
basic mathematical physics delivered to physics and engineering students, as well
as mathematics students in Italy, Germany and Luxembourg.
The book is mainly intended to be a self-contained introduction to the theory of
finite-dimensional vector spaces and linear transformations (matrices) with their
spectral analysis both on Euclidean and Hermitian spaces, to affine Euclidean
geometry as well as to quadratic forms and conic sections.
Many topics are introduced and motivated by examples, mostly from physics.
They show how a definition is natural and how the main theorems and results are
first of all plausible before a proof is given. Following this approach, the book
presents a number of examples and exercises, which are meant as a central part in
the development of the theory. They are all completely solved and intended both to
guide the student to appreciate the relevant formal structures and to give in several
cases a proof and a discussion, within a geometric formalism, of results from
physics, notably from mechanics (including celestial) and electromagnetism. | en_US |
