This book introduces the fundamental concepts of linear algebra and applies the theorems in computation-oriented applications. It is suitable for a one-semester course and combines definitions and proofs with a focus on computational applications. Examples illustrate the use of software packages such as Mathematica, Maple, and Sage. The journey begins with vector spaces and progresses through linear transformations and operators. It then covers orthogonal bases and matrix decomposition. The material includes a brief introduction to aspects of abstract algebra related to linear algebra, such as groups, rings, modules, fields, and polynomials over fields. Understanding these concepts is crucial for solving complex problems in various fields. This book transitions readers from basic definitions to advanced computational applications, blending theoretical knowledge with practical skills. It is an essential resource for mastering linear algebra and its applications

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