Basics Of Linear Algebra
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Basic Linear Algebra
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Author : T.S. Blyth
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Basic Linear Algebra written by T.S. Blyth and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations and complex numbers. Linear equations are treated via Hermite normal forms which provides a successful and concrete explanation of the notion of linear independence. Another important highlight is the connection between linear mappings and matrices leading to the change of basis theorem which opens the door to the notion of similarity. This new and revised edition features additional exercises and coverage of Cramer's rule (omitted from the first edition). However, it is the new, extra chapter on computer assistance that will be ofparticular interest to readers: this will take the form of a tutorial on the use of the "LinearAlgebra" package in MAPLE 7 and will deal with all the aspects of linear algebra developed within the book.
Basic Linear Algebra
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Author : Thomas S. Blyth
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Basic Linear Algebra written by Thomas S. Blyth and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Basic Linear Algebra is a text for first year students, working from concrete examples towards abstract theorems, via tutorial-type exercises. The book explains the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations, and complex numbers. Linear equations are treated via Hermite normal forms, which provides a successful and concrete explanation of the notion of linear independence. Another highlight is the connection between linear mappings and matrices, leading to the change of basis theorem which opens the door to the notion of similarity. The authors are well known algebraists with considerable experience of teaching introductory courses on linear algebra to students at St Andrews. This book is based on one previously published by Chapman and Hall, but it has been extensively updated to include further explanatory text and fully worked solutions to the exercises that all 1st year students should be able to answer.
Linear Algebra
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Author : Bernard R. Gelbaum
language : en
Publisher: North Holland
Release Date : 1989
Linear Algebra written by Bernard R. Gelbaum and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
Basics Of Linear Algebra
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Author : BILAL AHMAD DAR
language : en
Publisher: Shashwat Publication
Release Date : 2020-12-27
Basics Of Linear Algebra written by BILAL AHMAD DAR and has been published by Shashwat Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-27 with Juvenile Nonfiction categories.
This book intends to develop a sense of understanding towards Linear Algebra. It will introduce a beginner to the basic fundamentals of linear algebra and their properties. The definitions are explained thoroughly and for better understanding various examples have been put forth for each definition. For the practice of students, some examples and results have been kept in each chapter. Important points deduced from theorems are written as remarks for the benefit of students. This book is different from other books because of two main reasons. First, the book contains various solved examples which makes the particular topic more understandable. Second, a number of multiple choice questions/objectives with answer keys are kept for each chapter which will help the students to qualify various competitive examinations. The book consists of six chapters. The first chapter gives a brief introduction of matrices wherein various types of matrices with examples are mentioned. Also, the concept of determinants and adjoint of a matrix are explained briefly along with their properties. The second chapter deals with rank of a matrix, elementary transformations and elementary matrices. An important concept Echelon form of a matrix is mentioned and a method is introduced which explains how to determine rank of a matrix of any order. Third chapter deals with the linear dependence and independence of columns of a matrix and the behavior of matrix equation A X = O . A method is explained which tells how rank of a matrix gives information about the solution of Homogenous and Non-homogenous system of linear equations. Fourth chapter welcomes us with the central concept of linear algebra viz; Eigen values and Eigen vectors of a matrix. Many examples are solved which explains how many linearly independent Eigen vectors exist corresponding to an Eigen value and how to find them all.
Linear Algebra And Geometry
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Author : Al Cuoco
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-04-10
Linear Algebra And Geometry written by Al Cuoco and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-10 with Mathematics categories.
Linear Algebra and Geometry is organized around carefully sequenced problems that help students build both the tools and the habits that provide a solid basis for further study in mathematics. Requiring only high school algebra, it uses elementary geometry to build the beautiful edifice of results and methods that make linear algebra such an important field. The materials in Linear Algebra and Geometry have been used, field tested, and refined for over two decades. It is aimed at preservice and practicing high school mathematics teachers and advanced high school students looking for an addition to or replacement for calculus. Secondary teachers will find the emphasis on developing effective habits of mind especially helpful. The book is written in a friendly, approachable voice and contains nearly a thousand problems. An instructor's manual for this title is available electronically to those instructors who have adopted the textbook for classroom use. Please send email to [email protected] for more information.
Linear Algebra
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Author : Ward Cheney
language : en
Publisher: Jones & Bartlett Publishers
Release Date : 2012
Linear Algebra written by Ward Cheney and has been published by Jones & Bartlett Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
Ward Cheney and David Kincaid have developed Linear Algebra: Theory and Applications, Second Edition, a multi-faceted introductory textbook, which was motivated by their desire for a single text that meets the various requirements for differing courses within linear algebra. For theoretically-oriented students, the text guides them as they devise proofs and deal with abstractions by focusing on a comprehensive blend between theory and applications. For application-oriented science and engineering students, it contains numerous exercises that help them focus on understanding and learning not only vector spaces, matrices, and linear transformations, but uses of software tools available for use in applied linear algebra. Using a flexible design, it is an ideal textbook for instructors who wish to make their own choice regarding what material to emphasis, and to accentuate those choices with homework assignments from a large variety of exercises, both in the text and online.
Challenges And Strategies In Teaching Linear Algebra
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Author : Sepideh Stewart
language : en
Publisher: Springer
Release Date : 2018-02-01
Challenges And Strategies In Teaching Linear Algebra written by Sepideh Stewart and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-01 with Education categories.
This book originated from a Discussion Group (Teaching Linear Algebra) that was held at the 13th International Conference on Mathematics Education (ICME-13). The aim was to consider and highlight current efforts regarding research and instruction on teaching and learning linear algebra from around the world, and to spark new collaborations. As the outcome of the two-day discussion at ICME-13, this book focuses on the pedagogy of linear algebra with a particular emphasis on tasks that are productive for learning. The main themes addressed include: theoretical perspectives on the teaching and learning of linear algebra; empirical analyses related to learning particular content in linear algebra; the use of technology and dynamic geometry software; and pedagogical discussions of challenging linear algebra tasks. Drawing on the expertise of mathematics education researchers and research mathematicians with experience in teaching linear algebra, this book gathers work from nine countries: Austria, Germany, Israel, Ireland, Mexico, Slovenia, Turkey, the USA and Zimbabwe.
Ai Basics
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Author : Anand Vemula
language : en
Publisher: Anand Vemula
Release Date :
Ai Basics written by Anand Vemula and has been published by Anand Vemula this book supported file pdf, txt, epub, kindle and other format this book has been release on with Computers categories.
AI Basics is a comprehensive guide for anyone seeking to understand the foundational concepts, techniques, tools, and real-world applications of artificial intelligence. Structured across four parts, the book takes readers from the origins of AI to practical project development. Part I, Foundations of Artificial Intelligence, introduces core ideas such as the evolution of AI, types of intelligence (narrow, general, and superintelligence), and how AI differs from machine learning and deep learning. It also builds the mathematical and programming foundations necessary for AI, including linear algebra, probability, and Python-based development using essential libraries like NumPy and Scikit-learn. Part II, Core Techniques in AI, delves into machine learning and deep learning fundamentals. Readers learn about supervised and unsupervised learning, model training, overfitting, neural networks, backpropagation, and gradient descent. It also explores key domains like Natural Language Processing (NLP)—from text preprocessing to large language models—and Computer Vision, including CNNs and object detection. Part III, Tools and Applications, introduces platforms like TensorFlow, PyTorch, Jupyter Notebooks, and cloud AI services. It examines AI’s transformative impact in healthcare, finance, transportation, and robotics, while also addressing ethical concerns like bias, explainability, and regulation. Finally, Part IV, Building Your AI Journey, equips readers to develop and deploy AI projects. It outlines the full lifecycle—from defining problems and collecting data to model evaluation and deployment—emphasizing reproducibility, collaboration, and monitoring. This book is designed for students, professionals, and enthusiasts aiming to enter the world of AI with a strong, practical foundation.
The Art Of High Performance Computing For Computational Science Vol 1
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Author : Masaaki Geshi
language : en
Publisher: Springer
Release Date : 2019-05-14
The Art Of High Performance Computing For Computational Science Vol 1 written by Masaaki Geshi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-14 with Computers categories.
This book provides basic and practical techniques of parallel computing and related methods of numerical analysis for researchers who conduct numerical calculation and simulation. Although the techniques provided in this book are field-independent, these methods can be used in fields such as physics, chemistry, biology, earth sciences, space science, meteorology, disaster prevention, and manufacturing. In particular, those who develop software code in these areas will find this book useful. The contents are suitable for graduate students and researchers in computational science rather than novices at programming or informed experts in computer science. Starting with an introduction to the recent trends in computer architecture and parallel processing, Chapter 1 explains the basic knowledge of speedup programs with simple examples of numerical computing. Chapters 2 – 4 detail the basics of parallel programming, the message passing interface (MPI), and OpenMP and discuss hybrid parallelization techniques. Showing an actual example of adaptation, Chapter 5 gives an overview of performance tuning and communication optimizations. To deal with dense matrix calculations, Chapter 6 details the basics and practice of linear algebra calculation libraries BLAS and LAPACK, including some examples that can be easily reproduced by readers using free software. Focusing on sparse matrix calculations, Chapter 7 explains high performance algorithms for numerical linear algebra. Chapter 8 introduces the fast Fourier transform in large-scale systems from the basics. Chapter 9 explains optimization and related topics such as debug methods and version control systems. Chapter 10 discusses techniques for increasing computation accuracy as an essential topic in numerical calculation. This is the first of the two volumes that grew out of a series of lectures in the K computer project in Japan. The second volume will focus on advanced techniques and examples of applications in materials science.
Advanced Linear Algebra
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Author : Nicholas A. Loehr
language : en
Publisher: CRC Press
Release Date : 2024-06-21
Advanced Linear Algebra written by Nicholas A. Loehr and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-21 with Mathematics categories.
Designed for advanced undergraduate and beginning graduate students in linear or abstract algebra, Advanced Linear Algebra covers theoretical aspects of the subject, along with examples, computations, and proofs. It explores a variety of advanced topics in linear algebra that highlight the rich interconnections of the subject to geometry, algebra, analysis, combinatorics, numerical computation, and many other areas of mathematics. The author begins with chapters introducing basic notation for vector spaces, permutations, polynomials, and other algebraic structures. The following chapters are designed to be mostly independent of each other so that readers with different interests can jump directly to the topic they want. This is an unusual organization compared to many abstract algebra textbooks, which require readers to follow the order of chapters. Each chapter consists of a mathematical vignette devoted to the development of one specific topic. Some chapters look at introductory material from a sophisticated or abstract viewpoint, while others provide elementary expositions of more theoretical concepts. Several chapters offer unusual perspectives or novel treatments of standard results. A wide array of topics is included, ranging from concrete matrix theory (basic matrix computations, determinants, normal matrices, canonical forms, matrix factorizations, and numerical algorithms) to more abstract linear algebra (modules, Hilbert spaces, dual vector spaces, bilinear forms, principal ideal domains, universal mapping properties, and multilinear algebra). The book provides a bridge from elementary computational linear algebra to more advanced, abstract aspects of linear algebra needed in many areas of pure and applied mathematics.