Fundamentals of Linear Algebra and Analytical Geometry

238 95 6MB

English Pages [189] Year 1982

Author / Uploaded
Ya. S. Bugrov
S. M. Nikolsky

Table of contents :
Front Cover
Title Page
Contents
Preface
Sec. 1. Second-order Determinants
Sec. 2. Determinants of the Third and nth Order
Sec. 3. Matrices
Sec. 4. Systems of Linear Equations. The Kronecker-Capelli Theory
Sec. 5. Three-dimensional Space. Vectors. Cartesian System of Coordinates
Sec. 6. n-Dimensional Euclidean Space. Scalar Product of Two Vectors
Sec. 7. Segment of a Line. Dividing a Segment in a Given Ratio
Sec. 8. The Straight Line
Sec. 9. The Equation of a Plane
Sec. 10. A Straight Line in Space
Sec. 11. Orientation of Rectangular Coordinate Systems
Sec. 12. The Vector Product of Two Vectors
Sec. 13. Triple Scalar Product
Sec. 14. Linearly Independent System of Vectors
Sec. 15. Linear Operators
Sec. 16. Bases in R n
Sec. 17. Orthogonal Bases in Rn
Sec. 18. Invariant Properties of a Scalar and a Vector Product
Sec. 19. Transformation of Rectangular Coordinates in a Plane
Sec. 20. Linear Subspaces in Rn
Sec. 21. Fredholm-fype Theorems
Sec. 22. Self-adjoint Operator. Quadratic Form
Sec. 23. Quadratic Form in Two-dimensional Space
Sec. 24. Second-order Curves
Sec. 25. Second-order Surfaces in Three-dimensional Space
Sec. 26. The General Theory of a Second-order Surface in Three-Dimensional Space
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