Essential Linear Algebra for Postgraduates

This textbook strives to provide postgraduates and advanced undergraduates majoring in both mathematics and non-mathematics with new perspectives and novel approaches. The main goal is to help students, academic researchers and research and development (R&D) specialists master the most important and essential knowledge and skills of linear algebra for conquering the scientific and technological frontier, and for using this later in their careers in the era of artificial intelligence (AI). The text logically summarizes and reinforces the concepts, methods and conclusions of the analytic (or matrix) theory part that the reader has learned. Also, the text guides the reader to an appreciation of interrelations among different aspects and introduces some new concepts such as the gradient vector and Hessian matrix, which are often used in machine learning. The potential knowledge gaps, such as block matrix, matrix decompositions, and generalized inverse are gradually developed, properly compared, intuitively illustrated, and thoroughly explained. The textbook includes the feature examples that illustrate key concepts as well as exercises that strengthen understanding.