Linear Algebra I Basic Concepts

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Linear Algebra I Basic Concepts

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Author : Kazuo Murota
language : en
Publisher: World Scientific
Release Date : 2022-07-13

Linear Algebra I Basic Concepts written by Kazuo Murota and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-13 with Mathematics categories.

This is the first volume of the two-volume book on linear algebra, in the University of Tokyo (UTokyo) Engineering Course.The objective of this volume is to present, from the engineering viewpoint, the standard mathematical results in linear algebra such as those on systems of equations and eigenvalue problems. In addition to giving mathematical theorems and formulas, it explains how the mathematical concepts such as rank, eigenvalues, and singular values are linked to engineering applications and numerical computations.In particular, the following four aspects are emphasized.

Basic Concepts Of Linear Algebra

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Author : Samuel Isaak
language : en
Publisher: W. W. Norton
Release Date : 1976-02

Basic Concepts Of Linear Algebra written by Samuel Isaak and has been published by W. W. Norton this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976-02 with categories.

Essential Linear Algebra

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Author : Jared M. Maruskin
language : en
Publisher: Solar Crest Publishing LLC
Release Date : 2012-12

Essential Linear Algebra written by Jared M. Maruskin and has been published by Solar Crest Publishing LLC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12 with Mathematics categories.

This text introduces linear algebra--boiled to its essence--presented in a clear and concise fashion. Designed around a single-semester undergraduate course, Essential Linear Algebra introduces key concepts, various real-world applications, and provides detailed yet understandable proofs of key results that are aimed towards students with no advanced preparation in proof writing. The level of sophistication gradually increases from beginning to end in order to prepare students for subsequent studies.We begin with a detailed introduction to systems of linear equations and elementary row operations. We then advance to a discussion of linear transformations, which provide a second, more geometric, interpretation of the operation of matrix-vector product. We go on to introduce vector spaces and their subspaces, the image and kernel of a transformation, and change of coordinates. Following, we discuss matrices of orthogonal projections and orthogonal matrices. Our penultimate chapter is devoted to the theory of determinants, which are presented, first, in terms of area and volume expansion factors of 2x2 and 3x3 matrices, respectively. We use a geometric understanding of volume in n-dimensions to introduce general determinants axiomatically as multilinear, antisymmetric mappings, and prove existence and uniqueness. Our final chapter is devoted to the theory of eigenvalues and eigenvectors. We conclude with a number of discussions on various types of diagonalization: real, complex, and orthogonal.

Basic Concepts Of Calculus

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Author : John Meigs Hubbell Olmsted
language : en
Publisher:
Release Date : 1968

Basic Concepts Of Calculus written by John Meigs Hubbell Olmsted and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Calculus categories.

Linear Algebra And Its Applications

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Author : David C. Lay
language : en
Publisher: Addison Wesley Publishing Company
Release Date : 1994

Linear Algebra And Its Applications written by David C. Lay and has been published by Addison Wesley Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible.

Linear Algebra

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Author : Vivek Sahai
language : en
Publisher: CRC Press
Release Date : 2002-05

Linear Algebra written by Vivek Sahai and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-05 with Mathematics categories.

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.

Linear Algebra

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Author : Jin Ho Kwak
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Linear Algebra written by Jin Ho Kwak 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 2013-04-17 with Mathematics categories.

Linear algebra is one of the most important subjects in the study of science and engineering because of its widespread applications in social or natural science, computer science, physics, or economics. As one of the most useful courses in undergraduate mathematics, it has provided essential tools for industrial scientists. The basic concepts of linear algebra are vector spaces, linear transformations, matrices and determinants, and they serve as an abstract language for stating ideas and solving problems. This book is based on the lectures delivered several years in a sophomore level linear algebra course designed for science and engineering students. The primary purpose of this book is to give a careful presentation of the basic concepts of linear algebra as a coherent part of mathematics, and to illustrate its power and usefulness through applications to other disciplines. We have tried to emphasize the computational skills along with the mathematical abstractions, which have also an integrity and beauty of their own. The book includes a variety of interesting applications with many examples not only to help students understand new concepts but also to practice wide applications of the subject to such areas as differential equations, statistics, geometry, and physics. Some of those applications may not be central to the mathematical development and may be omitted or selected in a syllabus at the discretion of the instructor.

Modern Matrix Algebra

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Author : David Ross Hill
language : en
Publisher:
Release Date : 2001

Modern Matrix Algebra written by David Ross Hill and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

A recapitulation of his earlier work Seeds of Contemplation, this collection of sixteen essays plumbs aspects of human spirituality. Merton addresses those in search of enduring values, fulfillment, and salvation in prose that is, as always, inspiring and compassionate. “A stimulating series of spiritual reflections which will prove helpful for all struggling to...live the richest, fullest and noblest life” (Chicago Tribune).

A Course In Linear Algebra

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Author : David B. Damiano
language : en
Publisher: Harcourt Brace Jovanovich Incorporated
Release Date : 1988

A Course In Linear Algebra written by David B. Damiano and has been published by Harcourt Brace Jovanovich Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.

Introductory Linear Algebra

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Author : Maks Aĭzikovich Akivis
language : en
Publisher:
Release Date : 1972

Introductory Linear Algebra written by Maks Aĭzikovich Akivis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mathematics categories.