Elementary Linear Algebra
by Kenneth Kuttler
Publisher: The Saylor Foundation 2012
Number of pages: 433
This is an introduction to linear algebra. The main part of the book features row operations and everything is done in terms of the row reduced echelon form and specific algorithms. At the end, the more abstract notions of vector spaces and linear transformations on vector spaces are presented. However, this is intended to be a first course in linear algebra for students who are sophomores or juniors who have had a course in one variable calculus and a reasonable background in college algebra. I have given complete proofs of all the fundamental ideas but some topics such as Markov matrices are not complete in this book but receive a plausible introduction.
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The book was designed specifically for students who had not previously been exposed to mathematics as mathematicians view it. That is, as a subject whose goal is to rigorously prove theorems starting from clear consistent definitions.
by Ruslan Sharipov - Samizdat Press
This is a textbook of multidimensional geometry and linear algebra for the first year students. It covers linear vector spaces and linear mappings, linear operators, dual space, bilinear and quadratic forms, Euclidean spaces, Affine spaces.
by David Cherney, Tom Denton, Andrew Waldron - UC Davis
This textbook is suitable for a sophomore level linear algebra course taught in about twenty-five lectures. It is designed both for engineering and science majors, but has enough abstraction to be useful for potential math majors.
by Keith Matthews - University of Queensland
This an introduction to linear algebra with solutions to all exercises. It covers linear equations, matrices, subspaces, determinants, complex numbers, eigenvalues and eigenvectors, identifying second degree equations, three–dimensional geometry.