×

Principles of linear algebra with Maple. (English) Zbl 1211.65033

In the book the basics of linear algebra are presented, several applications are discussed and it is explained how one can use Maple for doing computations in linear algebra. In the first chapter a short introduction to Maple is given. In Chapters 2 and 3 matrix operations and methods for solving systems of linear algebraic equations are explained. Chapter 4 is devoted to the application of systems of linear equations and matrix multiplication in geometry, curve fitting, and economics. In Chapter 5 the computation of the determinant and the inverse of a matrix as well as Cramer’s rule are explained. The topics of Chapter 6 are vectors and operations with vectors. In Chapter 7 some problems of computer graphics are discussed, e.g. the rotation of surfaces and curves about any line passing through the origin.
Chapter 8 contains basics on dependent and independent sets of vectors as well as on the basis and dimension of subspaces.
In Chapters 9 and 10 linear maps are described by means of matrices and properties of the maps are discussed. Least-squares fits and pseudoinverses are the topics of Chapter 11. In the last chapter the computation of eigenvalues and eigenvectors is explained.
At the end of each section homework problems and Maple problems are formulated. The homework problems are problems which should be solved without Maple. These problems should deepen the understanding of the presented topics. Maple problems are problems which are computationally too expensive for solving by hand.

MSC:

65Fxx Numerical linear algebra
15-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra
15-04 Software, source code, etc. for problems pertaining to linear algebra
97H60 Linear algebra (educational aspects)
15A06 Linear equations (linear algebraic aspects)
65D10 Numerical smoothing, curve fitting
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
15A03 Vector spaces, linear dependence, rank, lineability
15A04 Linear transformations, semilinear transformations
15A09 Theory of matrix inversion and generalized inverses

Software:

Maple
PDFBibTeX XMLCite