Teaching Linear Algebra with and to Computers

Abstract

Three topics are discussed that relate to the teaching of linear algebra using computers (here the term computers includes calculators). The first topic is the variation in notation and terminology both between books and computer systems, and between di?erent computer systems. The second topic is the importance of numerical linear algebra, and how it becomes more di±cult to avoid numerical aspects of the subject once computers are used in teaching. The final topic is the Turing factoring of a matrix. This is a factoring approach to row reduction, and if it is taught in courses, students can transfer what they know to computers with a minimum of difficulty.