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This textbook is intended for students of Mathematical Economics and is based on my lectures on Linear Algebra delivered at Satbayev University in Almaty, Kazakhstan. The program closely aligns with that of the London School of Economics. The textbook extensively utilizes the concept of Gauss-Jordan elimination. Every subspace of the standard coordinate space possesses a unique Gauss basis. This observation significantly clarifies many aspects of Linear Algebra. The covered topics are outlined in the table of contents.
From the preface:
With the proliferation of Big Data Analysis, there has been an increased demand for education in Linear Algebra among economists. Unlike Calculus, Linear Algebra courses typically do not employ Descartes’ method of using Geometry for conceptual understanding and Algebra for computations, except in Analytic Geometry concerning lines and planes in space. I have observed that students often struggle with this aspect, as well as with grasping abstract concepts like vector space, bases, and subspaces. Therefore, this book adopts a traditional approach, treating Linear Algebra as a theory for solving finite systems of linear equations in a finite number of unknowns. Since every linear system can be represented by an augmented matrix, we focus on the study of matrices, – which being mere tables, are generally more accessible to students. Nowadays, students have access to tools like Wolfram’s Mathematica, Microsoft Math, and others. Additionally, ChatGPT Plus and Microsoft Copilot have emerged. As a result, numerical exercises such as calculating the reduced row echelon form of a matrix or the determinant of a square matrix or something else purely technical have diminished in value for grading student’s works. Such problems should be replaced with conceptual questions. This book suggests several ways to do this, offering, in particular, many solved economical problems. Some illustrate theoretical results, while others serve as exercises.
Foreword.
Preface.
Acknowledgements.
Gauss-Jordan Elimination.
Gauss Bases.
Inverse Matrices and Determinants.
Vector Spaces.
Diagonalization.
Inner Product Spaces.
Regression.
References.
Index