We now come to Fundamentals Of Linear Algebra And Analytical

Geometry by *Ya. S. Bugrov, S. M. Nikolsky.*

The present book is the first part of our three-part textbook

Higher-Mathematics. We deal here with the fundamentals of the theory

of deteminants, the elements of theory of matrices, the theory of

systems of linear equations, and vector algebra. The book is also

intended to introduce its readers to the basic aspects of linear

algebra: linear operators, orthogonal transformations, self-adjoint

operators, the quadratic forms and reducing it to the canonical

form. Elements of analytical geometry (the straight line, the plane,

the straight line in space, and second order curves and surfaces)are also included.

This book was translated from the Russian by *Leonid Levant* and

was first published by Mir Publishers in 1982.

*
*All credits to the

*original uploader.*

DJVU | 2.4 MB | Pages: 190 | dpi |

You can get the book here and *here.*

For magnet / torrent links go *here.*

Password if needed: *mirtitles*

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Facing problems while extracting? See *FAQs*

*Table of Contents*

**Preface 6**

1. Second Order Determinants 7

2. Determinants of third and n-th order 8

3. Matrices 19

4. Systems of Linear Equations. Kronecker-Capelli theory 21

5. Three dimensional Space. Vectors. Cartesian Systems of Coordinates 39

6. n-Dimensional Euclidean Space. Scalar Product of Two Vectors 48

7. Segment of a Line. Dividing a segment in a given ratio 53

8. The straight line 56

9. The Equation of a Plane 66

10. A Straight Line in Space 74

11. Orientation of Rectangular Coordinate Systems 78

12. The Vector Product of Two Vectors 81

13. Triple Scalar Product 87

14. Linearly Independent System of Vectors 89

15. Linear Operators 96

16. Bases in R_n 102

17. Orthogonal Bases in R_n 107

18. Invariant Properties of a Scalar and a Vector Product 113

19. Transformation of Rectangular Coordinates in a Plane 116

20. Linear Subspaces in R_n 119

21. Fredholm-type Theorems 125

22. Self-adjoint Operator. Quadratic Form 132

23. Quadratic Form in Two-dimensional Space 142

24. Second-order Curves 146

25. Second-order Surfaces in Three-dimensional Space 162

26. The General Theory of a Second-order Surface in Three-dimensional

Space 180

**Subject Index 187**

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Can i know the name of the third part of this series. I have only the second part which deals with Calculus.