With the inclusion of applications of singular value decomposition (SVD) and principal component analysis (PCA) to image compression and data analysis, this edition provides a strong foundation of linear algebra needed for a higher study in signal processing. The use of MATLAB in the study of linear algebra for a variety of computational purposes and the programmes provided in this text are the most attractive features of this book which strikingly distinguishes it from the existing linear algebra books needed as pre-requisites for the study of engineering subjects. This book is highly suitable for undergraduate as well as postgraduate students of mathematics, statistics, and all engineering disciplines. The book will also be useful to Ph.D. students for relevant mathematical resources.NEW TO THIS EDITION The Third Edition of this book includes: • Simultaneous diagonalization of two diagonalizable matrices • Comprehensive exposition of SVD with applications in shear analysis in engineering • Polar Decomposition of a matrix • Numerical experimentation with a colour and a black-and-white image compression using MATLAB • PCA methods of data analysis and image compression with a list of MATLAB codes

This book is the first of two volumes on linear algebra for graduate students in mathematics, the sciences, and economics, who have: a prior undergraduate course in the subject; a basic understanding of matrix algebra; and some proficiency with mathematical proofs. Proofs are emphasized and the overall objective is to understand the structure of linear operators as the key to solving problems in which they arise. This first volume re-examines basic notions of linear algebra: vector spaces, linear operators, duality, determinants, diagonalization, and inner product spaces, giving an overview of linear algebra with sufficient mathematical precision for advanced use of the subject. This book provides a nice and varied selection of exercises; examples are well-crafted and provide a clear understanding of the methods involved. New notions are well motivated and interdisciplinary connections are often provided, to give a more intuitive and complete vision of linear algebra. Computational aspects are fully covered, but the study of linear operators remains the focus of study in this book.

This is the second edition of the best-selling introduction to linear algebra. Presupposing no knowledge beyond calculus, it provides a thorough treatment of all the basic concepts, such as vector space, linear transformation and inner product. The concept of a quotient space is introduced and related to solutions of linear system of equations, and a simplified treatment of Jordan normal form is given.Numerous applications of linear algebra are described, including systems of linear recurrence relations, systems of linear differential equations, Markov processes, and the Method of Least Squares. An entirely new chapter on linear programing introduces the reader to the simplex algorithm with emphasis on understanding the theory behind it.The book is addressed to students who wish to learn linear algebra, as well as to professionals who need to use the methods of the subject in their own fields.

This book originates from the lessons held by the author in university courses and is aimed at students who, for the first time, are approaching a course in linear algebra and geometry. Bearing in mind the difficulties that students usually encounter in the study of abstract topics such as those presented in this book, we have chosen to use a language that is as simple as possible, trying to motivate the introduction of the various abstract notions with concrete examples. Topics covered include the theory of vector spaces and linear functions, the theory of matrices and systems of linear equations, the theory of Euclidean vector spaces and, finally, the applications of linear algebra to the study of the geometry of affine space. Numerous figures, examples and exercises carried out in every detail have been included in order to facilitate the study and understanding of the topics presented.

Enhance your NLP proficiency with modern frameworks like LangChain, explore mathematical foundations and code samples, and gain expert insights into current and future trends Key Features Learn how to build Python-driven solutions with a focus on NLP, LLMs, RAGs, and GPT Master embedding techniques and machine learning principles for real-world applications Understand the mathematical foundations of NLP and deep learning designs Purchase of the print or Kindle book includes a free PDF eBook Book DescriptionDo you want to master Natural Language Processing (NLP) but don’t know where to begin? This book will give you the right head start. Written by leaders in machine learning and NLP, Mastering NLP from Foundations to LLMs provides an in-depth introduction to techniques. Starting with the mathematical foundations of machine learning (ML), you’ll gradually progress to advanced NLP applications such as large language models (LLMs) and AI applications. You’ll get to grips with linear algebra, optimization, probability, and statistics, which are essential for understanding and implementing machine learning and NLP algorithms. You’ll also explore general machine learning techniques and find out how they relate to NLP. Next, you’ll learn how to preprocess text data, explore methods for cleaning and preparing text for analysis, and understand how to do text classification. You’ll get all of this and more along with complete Python code samples. By the end of the book, the advanced topics of LLMs’ theory, design, and applications will be discussed along with the future trends in NLP, which will feature expert opinions. You’ll also get to strengthen your practical skills by working on sample real-world NLP business problems and solutions.What you will learn Master the mathematical foundations of machine learning and NLP Implement advanced techniques for preprocessing text data and analysis Design ML-NLP systems in Python Model and classify text using traditional machine learning and deep learning methods Understand the theory and design of LLMs and their implementation for various applications in AI Explore NLP insights, trends, and expert opinions on its future direction and potential Who this book is for This book is for deep learning and machine learning researchers, NLP practitioners, ML/NLP educators, and STEM students. Professionals working with text data as part of their projects will also find plenty of useful information in this book. Beginner-level familiarity with machine learning and a basic working knowledge of Python will help you get the best out of this book.

This book presents a concise, comprehensive introduction to the fundamentals of linear algebra. The authors develop the subject in a manner accessible to readers of varied backgrounds. The material requires only very basic algebra and a rudimentary knowledge of matrices and determinants as prerequisites, but the text includes an introductory chapter containing most of the foundational material required. Linear Algebra begins with the basic concepts of vector spaces, subspace, basis, and dimension. Although the authors emphasize finite dimensional vector spaces, they also include examples of infinite dimensional vector spaces to highlight the differences between the two classes. The treatment then moves to the analysis of a single linear operator on a finite dimensional vector space, including discussions on characterizing diagonizable and triangulable operators. It uses the concept of generalized eigenvectors to obtain an inductive procedure for constructing a Jordan basis for a triangulable linear operator and again uses an algorithmic approach to the rational canonical form. Subsequent discussions focus on finite dimensional inner product spaces and non-negative operators, isometries, and polar and singular-value decomposition. The final chapter explores bilinear forms and extends the results of inner product spaces to bilinear spaces. Numerous examples and exercises at the end of each section make this an outstanding text for graduate and senior undergraduate students.

This book provides a self-contained and accessible introduction to linear and multilinear algebra. Besides the standard techniques for linear and multilinear algebra many advanced topics are included. Emphasis is placed on the Kronecker product and tensor product. The Kronecker product has widespread applications in signal processing, discrete wavelets, statistical physics, computer graphics, fractals, quantum mechanics and quantum computing. All these fields are covered in detail. A key feature of the book is the many detailed worked-out examples. Computer algebra applications are also given. Each chapter includes useful exercises. The book is well suited for pure and applied mathematicians as well as theoretical physicists and engineers.New topics added to the second edition are: braid-like relations, Clebsch-Gordan expansion, nearest Kronecker product, Clifford and Pauli group, universal enveloping algebra, computer algebra and Kronecker product.