This standalone book, now in a fully revised and expanded second edition, adopts a matrix-oriented approach to Linear Algebra. It presents a comprehensive theory, including all details and proofs, culminating in the Jordan normal form and its derivation. Throughout, the book emphasizes the practical application of the results. It also covers specific topics in Applied Linear Algebra, such as matrix functions, the diagonalization of matrices, the Kronecker product, and systems of linear matrix equations.

New to this edition are topics such as the Frobenius normal form and a more detailed presentation of infinite-dimensional vector spaces, along with many additional exercises. The matrix-oriented approach enhances understanding and simplifies abstract concepts, making them easier to grasp and apply in real-world situations. Major applications are illustrated through detailed examples.

Additionally, several "MATLAB Minutes" allow students to explore concepts and results through computational experiments, supported by a brief introduction to the basic principles of MATLAB. Along with more than 380 exercises, this encourages active engagement with the material.