Linear Algebra and Multi-Dimensional Geometry
N. V. Efimov, E. R. RozendornWe have tried to bear in mind the requirements of other mathematical disciplines and also of mechanics and physics. We hope that all parts of the text will be useful. The only preparation required for this text can be given an a firstsemester course of analytic geometry and algebra at the most elementary level. All that is needed is a firm grasp of the elements of these subjects. For Chapter XII the student should be acquainted with projective transformations and the projective properties of figures in the plane. Also, in Chapter X the reader may simplify his task by skipping Subsections 13 to 23 (Section 3) and Subsection 10 of Section 7. What is left of Chapter X can serve as a minimal algebraic basis for the theory of multidimensional integration.
It may be noted in conclusion that the first five chapters already contain material with broad applications in mathematics, mechanics, and physics. These chapters, supplemented with some of the material of subsequent chapters, can be utilized in higher technical schools with a more advanced mathematics curriculum.is a minimal algebraic basis for the theory of multidimensional integration.