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multilinear algebra – d g northcott multilinear algebra – werner greub multilinear algebra – marvin marcus multilinear algebra and differential forms for beginners

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Tensor Algebras Marcus Seminar Notes UCSB 1964 - 1969. Table of Contents[r]

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Tensor Spaces Marcus Seminar Notes UCSB 1964 - 1969

Table of Contents

1.1 Multilinear Functions 1

1.2 Free Spaces, Factor Spaces, Tensor Products 10

1.3 Properties of Tensor Spaces 21

1.4 Contraction, Extension, Inner Product 36

Index 51

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Chap 1 Tensor Spaces

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Tensor Spaces

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Tensor Transformations

Marcus Seminar Notes UCSB 1964 - 1969

Table of Contents

2.1 Tensor Products of Transformations 1

2.2 Properties of Mappings on Tensor Spaces 16

2.3 Symmetry Classes 36

2.4 Induced Transformations 65

Index 109

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Chap 2 Tensor Transformations

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Tensor Transformations

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Tensor Transformations

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Example 3.1(a) to (c),36,37

Example 3.2(a) to (d),42–45

Example 3.3(a) to (c),48–52

Example 4.1(a) to (c),66

Example 4.2(a) to (b),70

Example 4.3(a) to (c),73–75

Example 4.4(a) to (h),76–80

Example 4.5(a) to (d),82–84

Example 4.6(a) to (d),88–93

Example 4.7(a) to (c),96,97

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Tensor AlgebrasMarcus Seminar Notes UCSB 1964 - 1969

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Chap 3 Tensor Algebras

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Tensor Algebras

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Tensor Algebras

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Tensor Algebras

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Tensor Algebras

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Tensor Algebras

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Tensor Algebras

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Tensor Algebras

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Example 1.3(a) to (d),12–15

Example 1.4(a) to (b),16–23

Example 1.5(a) to (e),28–31

Example 2.1(a) to (b),50–52

Example 2.2,53,54

Example 2.3(a) to (e),55,56

Example 2.4(a) to (c),58–63

Example 2.5(a) to (d),63–65

Example 2.6(a) to (j),65–72

Example 2.7(a) to (b),72–74

Example 2.8(a) to(f),76–79

Example 2.9(a) to (d),82–86

G-graded algebra,3

G-graded vector space,3

Grassman orskew-symmetric algebra,19

homogeneoussubspace and ideal,4

124

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Iverson’s linear determinant,117

Laplace expansion theorem,30

k,54

pfaffian,121

principle of irrelevancealgebraic inequalities,97

skew-symmetric orGrassman algebra,19

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Exterior/Grassmann AlgebrasMarcus Seminar Notes UCSB 1965 - 1974

Table of Contents

4.1 Decomposibility 1

4.2 Duality in Exterior Algebras 61

4.3 Transformations on Grassmann Algebras 130

Index 165

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-400-350-300-250-200-150-100-50050100150200250300350400450500550600650700750800

Trang 393

-400-350-300-250-200-150-100-50050100150200250300350400450500550600650700750800

Trang 394

-400-350-300-250-200-150-100-50050100150200250300350400450500550600650700750800

Trang 395

-400-350-300-250-200-150-100-50050100150200250300350400450500550600650700750800

Trang 396

-400-350-300-250-200-150-100-50050100150200250300350400450500550600650700750800

Trang 397

-400-350-300-250-200-150-100-50050100150200250300350400450500550600650700750800

Trang 398

-400-350-300-250-200-150-100-50050100150200250300350400450500550600650700750800

Trang 399

-400-350-300-250-200-150-100-50050100150200250300350400450500550600650700750800

Trang 400

-400-350-300-250-200-150-100-50050100150200250300350400450500550600650700750800

Trang 401

-400-350-300-250-200-150-100-50050100150200250300350400450500550600650700750800

Trang 402

-400-350-300-250-200-150-100-50050100150200250300350400450500550600650700750800

Trang 403

-400-350-300-250-200-150-100-50050100150200250300350400450500550600650700750800

Trang 404

-400-350-300-250-200-150-100-50050100150200250300350400450500550600650700750800

Trang 405

-400-350-300-250-200-150-100-50050100150200250300350400450500550600650700750800

Trang 406

-400-350-300-250-200-150-100-50050100150200250300350400450500550600650700750800

Trang 407

-400-350-300-250-200-150-100-50050100150200250300350400450500550600650700750800

Trang 408

-400-350-300-250-200-150-100-50050100150200250300350400450500550600650700750800

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