Bugrov, Nikolsky – Fundamentals of Linear Algebra and Analytical Geometry

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

All credits to the original uploader.

DJVU | 2.4 MB | Pages: 190 | dpi |
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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
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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6 Responses to Bugrov, Nikolsky – Fundamentals of Linear Algebra and Analytical Geometry

1. Mir fan says:

U r back damitr,

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2. m95 says:

v great post many thanks

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3. restuarant says:

Hi, thanks for sharing.

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4. sharan1281 says:

tank u for publishing

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5. tiago says:

thank you so much for sharing.

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6. MathsMafia says:

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

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