A Modern Introduction to Linear Algebra

Text in English. 654 pp. "The author of this text, Henry Ricardo, has identified several shortcomings of typical courses on linear algebra and provides an exciting offering on how to overcome them . The key advantage of this text is that the crucial topic of eigenvalues and eigenvectors is reached as fast as possible! Chapter 4 is earlier than in most texts, and the integration of determinants within that chapter is a good way to keep that topic in the right place today. The single most exciting choice of this text is to start the semester with material on vectors (n-dimensional real vectors). This allows for a fast introduction to material that is new to students both to catch their interest and to demnonstrate that this class deals with material that is very new to most of them. And it sets up the entire text for the proper perspective in higher level mathematics of having vectors as elements of spaces" ? Matthias Gobbert, University of Maryland, Baltimore County, USA A Modern Introduction to Linear Algebra provides a rigorous yet accessible matrix-oriented introduction to the essential concepts of linear algebra. Concrete, easy-to-understand examples motivate the theory. The book first discusses vectors, Gaussian elimination, and reduced row echelon forms. It then offers a thorough introduction to matrix algebra, including defining the determinant naturally from he PA = LU factorization of a matrix. The author goes on to cover finite-dimensional real vector spaces, infinite dimensional spaces, linear transformations, and complex vector spaces. The Final chapter presents Hermitian and normal matrices as well as quadratic forms.…