This book is suited for a standard linear algebra course for engineering students at a bachelor level. Except for some basic algebra skills generally taught in secondary education, no prior knowledge is expected.

The main concepts of linear algebra are introduced from a geometrical perspective. We start by introducing the basic concepts of vectors, lines, and planes. There follows a thorough treatment of standard subjects like systems of linear equations, matrix arithmetic, eigenvalues and eigenvectors, orthogonality etc. In the final chapters, more advanced topics like symmetric matrices and discrete dynamical systems are discussed.

Throughout the book, many interactive applets are inserted to give the student hands-on experience with linear algebra. Thanks to an ample selection of embedded exercises with individualized feedback, the book offers a stimulating learning environment for studying linear algebra!@en

When does the complex product of a given number of subsets of a group generate the same subgroup as their union? We answer this question in a more general form by introducing HS-stability and characterising the HS-stable involution subsemigroup generated by a subset of a given involution semigroup. We study HS-stability for the special cases of regular ^∗-semigroups and commutative involution semigroups.

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In this paper, we describe an elementary method for counting the number of non-isomorphic algebras of a fixed, finite dimension over a given finite field. We show how this method works in the case of 2-dimensional algebras over the field F2.@en