Click on the cover image above to read some pages of this book! This book is a very good book for someone wanting to dive into Linear algebra. So many math books take a relatively simple topic and with the use of horrible notation and confused english, convert it to something esoteric and complicated. Matrices Definitions and Elementary Properties Matrix Multiplication Diagonal Matrices Special Real Matrices Special Complex Matrices Inverse and Systems of Matrices Determinants Inverse of a Matrix Systems of Matrices Rank of a Matrix Systems of Linear Equations Transformation of the Plane Mappings Rotations Reflections, Dilations, and Magnifications Other Transformations Linear Homogeneous Transformations Orthogonal Matrices Translations Rigid Motion Transformations Eigenvalues and Eigenvectors Characteristic Functions A Geometric Interpretaion of Eigenvectors Some Theorems Diagonalization of Matrices The Hamilton-Cayley Theorem Quadratic Forms Classification of the Conics Invariants for Conics Bibliography Answers to Odd-Numbered Exercises Index Table of Contents provided by Publisher. The purpose of this book is to familiarize the reader with the role of matrices in abstract algebraic systems, and to illustrate its effective use as a mathematical tool in geometry. You absolutely must take the time to learn everything as it's presented.
The major objects of study are matrices over an arbitrary field. I thought I could skim over the first chapter because I legitimately did know and remember all the concepts in it. Even though the course text was targeted toward social scientists like myself, its explanations and formula derivations were less helpful than its examples. Whereas all other linear algebra books talk about vector spaces and groups over the fields of real or complex numbers, Finkbeiner discusses other fields as well like the finite integer fields. If you have a course with a required text, you'll have to get it, and reviews won't matter much. There are also plenty of examples and exercises. This particular edition is in a Paperback format.
I heartily recommend it and suggest that you plow through it despite the horrible way it's written. Includes proofs of most theorems. Includes 16 sets of true-false quizzes and exercises — with worked-out solutions — a complete theory of permutations and much more. The book does cover some ideas not quite covered in other similar books, such as matrix analysis. The book says it has little in the way of prerequisites.
The concept of a linear transformation of the plane and the use of matrices in discussing such transformations are illustrated in Chapter. That's true in a strict sense, but in fact I think to use this book you need a certain amount of mathematical sophistication. Matrices are considered as elements of an algebra. This revised and corrected second edition of a classic book on special matrices provides researchers in numerical linear algebra and students of general computational mathematics with an essential reference. Here are the fundamental concepts of matrix algebra, first in an intuitive framework and then in a more formal manner. This book presents an elementary and concrete approach to linear algebra that is both useful and essential for the beginning student and teacher of mathematics.
This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. A great intro book to Matrices and Linear Transformations with tons of depth and great info. I know matrix multiplication, I know what row reduced echelon form is, I know the basics of solving systems of equations with matrices etc. A balanced combination of formal theory and related computational techniques, this treatment begins with the familiar problem of solving a system of linear equations. But for an overview or a quick review, this is a better book than Lay.
However, there is still some material in this book, such as canonical forms, that doesn't typically appear in introductory linear algebra books. In particular, the use of matrices in the study of transformations of the plane is stressed. Even Gilbert Strang's text on linear algebra is not quite as messy, in my opinion. The author introduces metric notions of Euclidean space at an early stage and employs the computational technique of Gaussian elimination throughout the book. Chapter 5 develops the Jordan canonical form using invariant subspaces and direct sum decompositions. Originally written for a series concerned with the mathematical training of teachers, and tested with hundreds of college students, this book can be used as a class or supplementary text for enrichments programs at the high school level, a one-semester college course, individual study, or for in-service programs.
If you want no-compromise, thorough learning, you'll get it, but you'll have to work for it. It's a highly affordable book and quite well written, which, I guess, is why they don't use this book to teach linear algebra in a 'modern' classroom. This is really a serious math textbook and without some significant understanding of how to read math books, you may have some studying to do beforehand. Although published over 40 years ago, this book is well written and organized. The author introduces metric notions of Euclidean space at an early stage and employs the computational technique of Gaussian elimination throughout the book. Cullen organizes his material well. The distinction between a latin letter to represent a scalar, a greek letter to represent a vector and an italic letter to represent a matrix was just too messed up.
I got this book to brush up on my linear algebra. Trust me, if you use this book, you will understand every single little tiny detail of matrices so incredibly well. The last section even covers numerical methods on matrices. Then you go back and realize those 10 steps could all be condensed into one simple theorem explained a couple subchapters back. It combines formal theory and related computational techniques. I approached this book as an engineer, meaning I just wanted a couple cheat sheets and quick algorithms to get out of it that I could then apply to a program, while chucking all the mathematical formality and notation out the window. I found Cullen's book and it got me through the course.