Finite-Dimensional Vector Spaces and Matrices
In the present chapter we examine some of the properties of finite-dimensional linear spaces. We will show how elements of such spaces are represented by coordinate vectors and how linear transformations on such spaces are represented by means of matrices. We then will study some of the important properties of matrices. Also, we will investigate in some detail a special type of vector space, called the Euclidean space. This space is one of the most important spaces encountered in applied mathematics.
KeywordsDinate Rile pTAP
Unable to display preview. Download preview PDF.
- [4.2]R. E. Bellman, Introduction to Matrix Algebra. New York: McGraw-Hill Book Company, Inc., 1970.Google Scholar
- [4.3]F. Brauer and J. A. Nohel, Qualitative Theory of Ordinary Differential Equations: An Introduction. New York: W. A. Benjamin, Inc., 1969.Google Scholar
- [4.8]K. Hoffman and R. Kunze, Linear Algebra. Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1961.Google Scholar
- [4.9]S. Lipschutz, Linear Algebra. New York: McGraw-Hill Book Company, 1968.Google Scholar
- [4.11]L. S. Pontriagin, Ordinary Differential Equations. Reading, Mass.: Addison-Wesley Publishing Co., Inc., 1962.Google Scholar