Euclidean Linear Algebra

Euclidean Linear Algebra offers a concise and theoretical introduction to linear algebra with a plethora of examples, a wide variety of problems, and preparation for more advanced mathematics rather than external applications. This text provides purely computational exercises and theoretical problems ranked by difficulty, allowing for a balance between computational practice and the development of critical thinking and theoretical mathematical thought.

To support the emphasis on linear maps, linear maps are introduced immediately after the necessary background on linear systems and vectors. Additional chapters explore properties of linear maps, the image and kernel of linear maps, operations on linear maps, subspaces and dimension and their relationships to linear maps, different forms of subspaces and how they allow us to intersect and add subspaces, projection maps, eigenvalues and eigenvectors of linear maps, changing coordinates of linear maps, diagonalizing linear maps, coordinate independence, orthogonality, orthogonal projections, isometries, adjoints of linear maps, and linear algebra with polynomials, sequences, and over the complex numbers. An appendix supports student learning with a definitions reference, an objects chart, an introduction to proof frameworks, and answers to selected exercises.

Developed to guide beginner students, Euclidean Linear Algebra is an ideal resource for programs and courses in mathematics. Sheldon Axler's Linear Algebra Done Right is a great follow up for a secondary course in linear algebra.

Connor Thomas Ahlbach is a mathematics lecturer at Texas State University, where he regularly teaches algebra, calculus, and linear algebra. He holds a Ph.D. from the University of Washington. His research interests include combinatorics and algebraic combinatorics. Dr. Ahlbach's research has appeared in Journal of Combinatorics, European Journal of Combinatorics, and Journal of Algebraic Combinatorics.