Linear Algebra

In his new undergraduate textbook, Harold M. Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra. Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century. Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience. Designed for a one-semester course, this text adopts an algorithmic approach to linear algebra giving the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject. Students at all levels will find much interactive instruction in this text while teachers will find stimulating examples and methods of approach to the subject. In this undergraduate textbook, Harold M. Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra. Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century. Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience Front Matter....Pages i-xiii Matrix Multiplication....Pages 1-9 Equivalence of Matrices. Reduction to Diagonal Form....Pages 10-24 Matrix Division....Pages 25-33 Determinants....Pages 34-49 Testing for Equivalence....Pages 50-59 Matrices with Rational Number Entries....Pages 60-67 The Method of Least Squares....Pages 68-77 Matrices with Polynomial Entries....Pages 78-90 Similarity of Matrices....Pages 91-110 The Spectral Theorem....Pages 111-131 Back Matter....Pages 132-184 * Proposes a radically new and thoroughly algorithmic approach to linear algebra * Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples * Designed for a one-semester course, this text gives the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject Linear Algebra is a text for a one-semester course that is given in every undergraduate university and college curriculum. This book adopts an algorithmic approach, giving the student many examples to work through and exercises to test their skill and extend their knowledge of the subject.