There are plenty of textbooks both in German and in English on the
topic of linear algebra, at various levels but also differing widely
with respect to comprehensiveness and structure.
Students are encouraged to explore which books suit their tastes.
Most relevant books are available in the mathematics library, which has
a shelf in the reading room dedicated to linear algebra and one with
English books especially for the MCS students. (There is also a
section with mathematical dictionaries.)
Some suggestions (from the library):
Anton: Elementary Linear Algebra, 7th edition, Wiley
also in German translation, Spektrum Verlag.
Artmann: Lineare Algebra, Birkhäuser
Beutelsbacher: Lineare Algebra, Vieweg
Brieskorn: Lineare Algebra und Analytische Geometrie (I,II), Vieweg
Bröcker: Lineare Algebra und Analytische Geometrie, Birkhäuser
Curtis: Linear Algebra  An Introductory Approach, Springer
Fischer: Lineare Algebra, 11. Aufl., Vieweg
Greub: Linear Algebra, Springer
there is also a German edition
Jänich: Lineare Algebra, 10. Aufl., Springer
also in English translation, Springer
Kaye, Wilson: Linear Algebra, Oxford University Press
Klingenberg, Klein: Lineare Algebra und Analytische Geometrie, BI
Koecher: Lineare Algebra und Analytische Geometrie, Springer
Kwak, Hong: Linear Algebra, Birkhäuser
Lingenberg: Lineare Algebra, BI
Strang: Linear Algebra and its Applications, Academic Press
