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Introduction to algebra
Book II
Linear algebra
[
154
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53%
]
A. I. Kostrikin
On this page
▸
II.1 · Spaces and forms
▸
II.2 · Linear operators
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II.3 · Vector spaces with a scalar product
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II.4 · Affine and Euclidean point spaces
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II.5 · Quadrics
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II.6 · Tensors
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II.7 · Applications
Chapter II.1
Spaces and forms
[
24
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17%
]
Section II.1.1
Abstract vector spaces
[
2
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0%
]
Section II.1.2
Dimension and basis
[
12
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17%
]
Section II.1.3
Dual space
[
5
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0%
]
Section II.1.4
Bilinear and quadratic forms
[
5
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40%
]
Chapter II.2
Linear operators
[
38
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71%
]
Section II.2.1
Linear mappings of vector spaces
[
3
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33%
]
Section II.2.2
Algebra of linear operators
[
12
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50%
]
Section II.2.3
Invariant subspaces and eigenvectors
[
10
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80%
]
Section II.2.4
Jordan normal form
[
13
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92%
]
Chapter II.3
Vector spaces with a scalar product
[
35
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71%
]
Section II.3.1
Euclidean vector spaces
[
8
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100%
]
Section II.3.2
Hermitian vector spaces
[
3
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33%
]
Section II.3.3
Linear operators on spaces with a scalar product
[
13
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92%
]
Section II.3.4
Complexification and realification
[
4
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50%
]
Section II.3.5
Orthogonal polynomials
[
7
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29%
]
Chapter II.4
Affine and Euclidean point spaces
[
16
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44%
]
Section II.4.1
Affine spaces
[
6
/
33%
]
Section II.4.2
Euclidean
[
3
/
67%
]
Section II.4.3
Groups and geometries
[
3
/
100%
]
Section II.4.4
Spaces with an indefinite metric
[
4
/
0%
]
Chapter II.5
Quadrics
[
14
/
29%
]
Section II.5.1
Quadratic functions
[
2
/
0%
]
Section II.5.2
Quadrics in affine and Euclidean spaces
[
7
/
57%
]
Section II.5.3
Projective spaces
[
3
/
0%
]
Section II.5.4
Quadrics in projective space
[
2
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0%
]
Chapter II.6
Tensors
[
15
/
40%
]
Section II.6.1
The beginnings of tensor calculus
[
7
/
57%
]
Section II.6.2
Tensor contraction, symmetrization, and alternation
[
3
/
0%
]
Section II.6.3
Exterior algebra
[
5
/
40%
]
Chapter II.7
Applications
[
12
/
67%
]
Section II.7.1
The norm and functions of a linear operator
[
10
/
70%
]
Section II.7.2
Linear differential equations
Section II.7.3
Convex polyhedra and linear programming
[
2
/
50%
]
Section II.7.4
Non-negative matrices
Section II.7.5
Lobachevsky geometry
Section II.7.6
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