A Matrix Algebra Approach to Artificial Intelligence

1. Front Matter

   Pages i-xxxiv

   PDF

2. Introduction to Matrix Algebra

   1. Front Matter

      Pages 1-1

      PDF

   2. Basic Matrix Computation

      • Xian-Da Zhang

      Pages 3-54

   3. Matrix Differential

      • Xian-Da Zhang

      Pages 55-87

   4. Gradient and Optimization

      • Xian-Da Zhang

      Pages 89-155

   5. Solution of Linear Systems

      • Xian-Da Zhang

      Pages 157-201

   6. Eigenvalue Decomposition

      • Xian-Da Zhang

      Pages 203-220

3. Artificial Intelligence

   1. Front Matter

      Pages 221-221

      PDF

   2. Machine Learning

      • Xian-Da Zhang

      Pages 223-440

   3. Neural Networks

      • Xian-Da Zhang

      Pages 441-615

   4. Support Vector Machines

      • Xian-Da Zhang

      Pages 617-679

   5. Evolutionary Computation

      • Xian-Da Zhang

      Pages 681-803

4. Back Matter

   Pages 805-820

   PDF

Matrix algebra plays an important role in many core artificial intelligence (AI) areas, including machine learning, neural networks, support vector machines (SVMs) and evolutionary computation. This book offers a comprehensive and in-depth discussion of matrix algebra theory and methods for these four core areas of AI, while also approaching AI from a theoretical matrix algebra perspective.

The book consists of two parts: the first discusses the fundamentals of matrix algebra in detail, while the second focuses on the applications of matrix algebra approaches in AI. Highlighting matrix algebra in graph-based learning and embedding, network embedding, convolutional neural networks and Pareto optimization theory, and discussing recent topics and advances, the book offers a valuable resource for scientists, engineers, and graduate students in various disciplines, including, but not limited to, computer science, mathematics and engineering.  

• Matrix Algebra
• Artificial Intelligence
• Linear Algebra
• Machine Learning
• Neural Networks
• Evolutionary Computation
• Learning Systems
• Learning Algorithms
• Support Vector Machine
• matrix theory

“The book is of very high relevance for students, professors and researchers involved in artificial intelligence (AI), the work is also of very high relevance for the mathematics community in general since it addresses the importance of matrix algebra for the field of AI and how major approaches and state-of-the-art algorithms rely on matrix algebra.” (Carlos Pedro Gonçalves, zbMATH 1455.68010, 2021)

• Department of Automation, Tsinghua University, Beijing, China

  Xian-Da Zhang

XIAN-DA ZHANG is a Professor Emeritus at the Department of Automation, Tsinghua University, China. He was a Distinguished Professor at Xidian University, Xi’an, China, as part of the Ministry of Education of China and Cheung Kong Scholars Programme, from 1999 to 2002. His areas of research include intelligent signal and information processing, pattern recognition, machine learning and neural networks, evolutional computation, and correlated applied mathematics. He has published over 120 international journal and conference papers. The Japanese translation of his book “Linear Algebra in Signal Processing” (published in Chinese by Science Press, Beijing, in 1997) was published by Morikita Press, Tokyo, in 2008. He also authored the book “Matrix Analysis and Applications” (Cambridge University Press, UK, 2017).

Policies and ethics