Linear Algebra (Book)

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Linear Algebra
Information
Author	Georgi Shilov
Language	English
Publisher	Dover Publications
Publication Date	1 June 1977
Pages	400
ISBN-10	048663518X
ISBN-13	978-0486635187

The textbook Linear Algebra by Georgi Shilov provides a thorough introduction to linear algebra.

Table of Contents

Chapter/Section #	Title	Page #
Chapter 1: Determinants
1.1	Number Fields	1
1.2	Problems of the Theory of Systems of Linear Equations	3
1.3	Determinants of Order \(n\)	5
1.4	Properties of Determinants	8
1.5	Cofactors and Minors	12
1.6	Practical Evaluation of Determinants	16
1.7	Cramer's Rule	18
1.8	Minors of Arbitrary Order. Laplace's Theorem	20
1.9	Multiplicative inverses	23
	Problems	28
Chapter 2: Linear Equations
1	Equations in two unknowns	53
2	Equations in three unknowns	57
Chapter 3: Real Numbers
1	Addition and multiplication	61
2	Real numbers: positivity	64
3	Powers and roots	70
4	Inequalities	75
Chapter 4: Quadratic Equations
Interlude: On Logic and Mathematical Expressions
1	On reading books	93
2	Logic	94
3	Sets and elements	99
4	Notation	100
PART II: INTUITIVE GEOMETRY
Chapter 5: Distance and Angles
1	Distance	107
2	Angles	110
3	The Pythagoras theorem	120
Chapter 6: Isometries
1	Some standard mappings of the plane	133
2	Isometries	143
3	Composition of isometries	150
4	Inverse of isometries	155
5	Characterization of isometries	163
6	Congruences	166
Chapter 7: Area and Applications
1	Area of a disc of radius r	173
2	Circumference of a circle of radius r	180
PART III: COORDINATE GEOMETRY
Chapter 8: Coordinates and Geometry
1	Coordinate systems	191
2	Distance between points	197
3	Equation of a circle	203
4	Rational points on a circle	206
Chapter 9: Operations on Points
1	Dilations and reflections	213
2	Addition, subtraction, and the parallelogram law	218
Chapter 10: Segments, Rays, and Lines
1	Segments	229
2	Rays	231
3	Lines	236
4	Ordinary equation for a line	246
Chapter 11: Trigonometry
1	Radian measure	249
2	Sine and cosine	252
3	The graphs	264
4	The tangent	266
5	Addition formulas	272
6	Rotations	277
Chapter 12: Some Analytic Geometry
1	The straight line again	281
2	The parabola	291
3	The ellipse	297
4	The hyperbola	300
5	Rotation of hyperbolas	305
PART IV: MISCELLANEOUS
Chapter 13: Functions
1	Definition of a function	313
2	Polynomial functions	318
3	Graphs of functions	330
4	Exponential function	333
5	Logarithms	338
Chapter 14: Mappings
1	Definition	345
2	Formalism of mappings	351
3	Permutations	359
Chapter 15: Complex Numbers
1	The complex plane	375
2	Polar form	380
Chapter 16: Induction and Summations
1	Induction	383
2	Summations	388
3	Geometric series	396
Chapter 17: Determinants
1	Matrices	401
2	Determinants of order 2	406
3	Properties of 2 x 2 determinants	409
4	Determinants of order 3	414
5	Properties of 3 x 3 determinants	418
6	Cramer's Rule	424
Index		429