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Introduction to algebra
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II · Linear algebra
Chapter II.6
Tensors
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II.6.1 · The beginnings of tensor calculus
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II.6.2 · Tensor contraction, symmetrization, and alternation
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II.6.3 · Exterior algebra
Section II.6.1
The beginnings of tensor calculus
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Subsection II.6.1.1
The concept of tensors
Subsection II.6.1.2
Tensor product
Subsection II.6.1.3
Tensor coordinates
Subsection II.6.1.4
Tensors in different coordinate systems
Subsection II.6.1.5
Tensor product of spaces
Section II.6.2
Tensor contraction, symmetrization, and alternation
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Subsection II.6.2.1
Tensor contraction
Subsection II.6.2.2
Structural tensor of the algebra
Subsection II.6.2.3
Symmetric tensors
Subsection II.6.2.4
Skew-symmetric tensors
Subsection II.6.2.5
Tensor spaces
Section II.6.3
Exterior algebra
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Subsection II.6.3.1
Exterior multiplication
Subsection II.6.3.2
Exterior algebra of a vector space
Subsection II.6.3.3
Connection with determinants
Subsection II.6.3.4
Vector subspaces and p-vectors
Subsection II.6.3.5
Conditions for the decomposability of p-vectors