This book, linear algebra problem book, is perhaps best described as an engaging and semiinformal invitation and complement to that original. Linear algebra1 linear algebra linear algebra is the branch of mathematics concerning finite or countably infinite dimensional vector spaces, as well as linear mappings between such spaces. This clear, concise and highly readable text is designed for a first course in linear algebra and is intended linear algebra. Finitedimensional vector spaces undergraduate texts in.
Linear algebra a modern introduction 4th revised edition. Linear algebra a modern introduction 4th revised edition by. Second edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. Nov 24, 2010 primer of linear algebra, notes for math 4050, math 80006, math 84345, and the linear algebra is in 845. Nov 18, 2015 speaking of hoffman and kunze, and halmos linear algebra problem book, how do those two compare as a main textbook.
By the way, saying a linear algebra book does a good job on everything except jordan form, is like saying a calculus book does a good job on everything except integration, i. Every time ive taught the course undergraduate, ive been saddled with someone elses choice of text. Can one learn linear algebra solely by solving problems. Linear algebra 2nd edition by kenneth hoffman and ray kunze. Linear algebracomplex vector spaces wikibooks, open books. Such an investigation is initially motivated by a system of linear equations in several unknowns. Linear algebra 2nd edition by hoffman and kunz prentice hall. Halmos linear algebra problem book isnt meant as a main textbook. Iirc it is available as pdf on the internet for free. If you would follow the road to linear algebra here are some trustworthy signposts. In modern mathematics, the presentation through vector spaces is generally preferred, since it is more synthetic, more general not limited to the finitedimensional case, and conceptually simpler, although more abstract a vector space over a field f often the field of the real numbers. A concise text on advanced linear algebra by yisong yang. Paul halmos thinks so, and you will too once you read this book. Nonhomogeneous systems of linear equations 100,143 chapter 5 linear operators and matrices 108 598 5.
Linear transformations, the kernel and range of a linear transformation, ranknullity theorem, algebra of linear transformations,isomorphism, representation of transformations by matrices, linear functional, dual and double dual of a space, annihilator of a subset, transpose of a linear transformation. Linear algebra mathematical association of america. Linear algebra and its applications 5th edition by lay mcdonald solution manual 1 chapters updated mar 27, 2019 06. Mar 26, 2018 linear algebra1 linear algebra linear algebra is the branch of mathematics concerning finite or countably infinite dimensional vector spaces, as well as linear mappings between such spaces. Linear algebra problem book can be either the main course or the dessert for someone who needs linear algebra and nowadays that means every user of mathematics. This book develops linear algebra the way mathematicians see it. It can be used as the basis of either an official course or a program of private study.
Buy from amazon my personal pick for a second course one of my favoraite books on linear algebra. Master expositor paul halmos presents linear algebra in the pure axiomatic spirit. So im going with speculation here in terms of what i think. Please refer a problem book on linear algebra containing the following topics. The reason its not on the list is i just didnt see what it had to offer that isnt covered in later books. March 3, 1916 october 2, 2006 was a hungarianborn american mathematician and statistician who made fundamental advances in the areas of mathematical logic, probability theory, statistics, operator theory, ergodic theory, and functional analysis in particular, hilbert spaces. Linear algebra done right is a good introduction, but if you want to go beyond an undergraduate level, try linear algebra by hoffman and kunze. Until the 19th century, linear algebra was introduced through systems of linear equations and matrices. Strang, linear algebra and its applications 4th edition, thom. We shall develop the material of linear algebra and use it as setting for the relevant material of intermediate calculus. In exercise 6 of this section they ask us to show, in the special case of two equations and two unknowns, that two homogeneous linear systems have the exact same solutions then they have the same rowreduced echelon form we know the converse is always true by theorem 3, page 7. As mentioned above linear algebra 2nd edition by kenneth m hoffman and ray kunze. Linear transformations, the kernel and range of a linear transformation, ranknullity theorem, algebra of linear transformations,isomorphism, representation of transformations by matrices, linear functional, dual and double dual of a space, annihilator of a subset. March 3, 1916 october 2, 2006 was a hungarianborn american mathematician and statistician who made fundamental.
Anton, elementary linear algebra with applications 8th edition, john wiley 1995. It takes the student step by step from the basic axioms of a field through the notion of vector spaces, on to advanced concepts such as inner product spaces and normality. Matrix analysis and topics in matrix analysis by roger a. The text actually attempts to understand the properties of linear operators, and proves theorems such as primary decomposition theorem, cyclic decomposition theorem. Problem book on linear algebra mathematics stack exchange. Vector spaces, linear dependence of vectors, basis, dimension, linear transformations, matrix representation with respect to an ordered basis, range space and null space, ranknullity theorem. Advanced linear algebra beyond a first course most of these will probably be more accessible to someone who has read one of the above intro books, and axlers linear algebra done right. Paul halmos thinks so, and you will too once you read this. The techniques taught are meant to be generalizable to the infinite dimensional cases i.
Halmos equally enjoyable companion linear algebra problem book, published by ama, 1995, is a bonus icing on the cake. As a linear algebra refresher, i am working through the above cited text 2nd ed. Though old and classical, it is one of the best linear algebra books for math major students. Very few formal prerequisites are needed to read this, but some mathematical maturity is necessary. Linear algebra, 2nd edition kenneth hoffmann and ray kunze pdf. Ma 6102 linear algebra national institute of technology calicut. Regarding hoffmankunze, suffice it to say that all undergraduatelevel material is done the right way and then some, meaning that everything is proved, very carefully and with no compromises, and material is dealt with that is most often introduced no earlier than in graduate algebra, or possibly in an honors course in advanced linear algebra. The linear algebra problem book is an ideal text for a course in linear algebra. No need to wait for office hours or assignments to be graded to find out where you took a wrong turn. I do have halmos linear algebra problem book on the list because its quite good. Our subject matter is intermediate calculus and linear algebra. Additionally, the book includes ample applications drawn from a variety of disciplines, which reinforce the fact that linear algebra is a valuable tool for modeling reallife problems.
Based almost solely on proofs and most of the exercises are proof based, although the beginning ones of each section are computational. In modern mathematics, the presentation through vector spaces is generally preferred, since it is more synthetic, more general not limited to the finitedimensional case, and conceptually simpler, although more abstract. Introduction to linear algebra, by hoffman and kunge. Linear algebra kenneth hoffman professor of mathematics massachusetts institute of technology ray kunze professor of mathematics university of california, irvine second edition prenticehall, inc. The definition of a linear operator, the image and kernel of an. Unlike static pdf linear algebra solution manuals or printed answer keys, our experts show you how to solve each problem stepbystep.
Linear algebra has in recent years become an essential part of the mathematical background required by mathematicians and mathematics teachers, engineers, computer scientists, physicists, economists, and statisticians, among others. Chapter 4 defines the algebra of polynomials over a field, the ideals in that algebra, and the prime factorization of a polynomial. In addition to thorough coverage of linear equations, matrices, vector spaces, game theory, and numerical. These notes do assume that the reader has a good working knowledge of basic algebra. And for those more interested in applications both elementary linear algebra. Finite dimensional vector spaces by halmos is an excellent book in linear algebra. Linear algebracomplex vector spaces wikibooks, open. About the authordavid poole is professor of mathematics at trent university, where he has been a faculty member since 1984. Buy linear algebra problem book dolciani mathematical. A book that is absolutely terrific for selfstudy is halmoss linear algebra problem book. And theyve generally been isomorphic the same and not particularly inspiring. Applications version 1 by howard anton and chris rorres and linear algebra and its applications 10 by gilbert strang are loaded with applications.
This may be my favorite text because of its volume of content. It also deals with roots, taylors formula, and the lagrange inter polation. Despite the fact that these are my class notes they should be accessible to anyone wanting to learn linear algebra or needing a refresher. It is one of the first linear algebra books in a modern style, being published in 1958. Speaking of hoffman and kunze, and halmos linear algebra problem book, how do those two compare as a main textbook. Jan 01, 1995 paul halmos thinks so, and you will too once you read this book. Linear algebra dover books on mathematics by georgi e. Halmos is one of the great mathematical expositors of the 20th century, and his book finite dimensional vector spaces stands as the definitive introduction to the subject for budding mathematicians.