Introduction To Linear Algebra 5th Edition Johnson Solutions
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This is an erudite and discursive introduction to linear algebra, weighted heavily toward matrices and systems of linear equations. The author has an expansive view of linear algebra, and from time to time draws in some calculus, Fourier series, wavelets, and function spaces, but the approach is always very concrete. The book doesn't skimp on the techniques of linear algebra, and there are seemingly endless examples of LU-decomposition and other numeric work, as well as a fairly extensive Chapter 9 on numerical methods. But the book also does a good job of moving up and down between various levels of abstraction, according to which level makes the problem at hand easier to comprehend, and geometrical examples and rotations play an important role in the exposition.
(My personal pick for a first course) This is a no-frills textbook for a one-semester course in linear algebra that focuses very heavily on algorithms and applications. Despite the no-frills approach, it is still a long book and it covers everything that would normally be in an introductory course, and a lot that would not be. There is much more material here than could be covered in a semester.
The breadth of applications is especially impressive: although most of them use extremely simplified models of the thing being studied, they really do give you a good understanding of how linear algebra is used in practice. The applications cover many areas of science, business, and engineering, with a lot of dynamical systems examples. There are also many notes on numerical considerations. None of this goes into enough depth to make you an expert (that would be impossible in a one-semester introductory course), or even able to tackle such applications on your own, but it does give you a good understanding of how linear algebra is used and why it is important.
(My personal pick for a second course) One of my favoraite books on Linear Algebra. This book can be thought of as a very pure-math version of linear algebra, with no applications and hardly any work on matrices, determinants, or systems of linear equations. Instead it focuses on linear operators, primarily in finite-dimensional spaces but in many cases for general vector spaces. Solutions can be found here.
(My personal pick for a second course) One of my favoraite books on Linear Algebra. Though old and classical, it is one of the best linear algebra books for math major students. Solutions can be found here.
Regarding Hoffman-Kunze, suffice it to say that all undergraduate-level 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.
I want to lament in this connection that over recent decades a shift has occurred regarding linear algebra: things once covered in lower division work are now part of the standard graduate course, and accordingly erstwhile solidly undergraduate linear algebra, e.g., the full discussion of the eigenvalue problem leading to the Jordan canonical form, have fallen off the undergraduate table. The result is that this fantastic book is not usable in most undergraduate linear algebra courses. But it is an unsurpassed text for highly gifted kids who intend to do graduate school right and then go on to do real mathematics.
This is a classic but still useful introduction to modern linear algebra. It is primarily about linear transformations, and despite the title most of the theorems and proofs work for arbitrary vector spaces.
This seems to be the standard choice for honors undergraduate courses in the US these days. It is more challenging than the usual computational type introductions to linear algebra. If you want something more applied and less theoretical than the above three books, this is the best linear algebra textbook for you.
(My personal pick for reference) This is a formidable volume, a compendium of linear algebra theory, classical and modern, intended for "the graduate or advanced undergraduate student." (I have not had the privilege of teaching undergraduates who could handle this text.) After a concise (30-page) treatment of set theory and basic algebraic structures, the author embarks on a two-chapter whirlwind tour of introductory linear algebra, including an optional discussion of topological vector spaces. Following this, there are several chapters of module theory, leading to structure theorems for finite-dimensional linear operators. The last parts of the "Basic Linear Algebra" section of the book are devoted to real and complex inner product spaces and the structure of normal operators. 2b1af7f3a8