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Olariu S. — Complex Numbers in n Dimensions
Olariu S. — Complex Numbers in n Dimensions



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Название: Complex Numbers in n Dimensions

Автор: Olariu S.

Аннотация:

Two distinct systems of hypercomplex numbers in n dimensions are introduced in this book, for which the multiplication is associative and commutative, and which are rich enough in properties such that exponential and trigonometric forms exist and the concepts of analytic n-complex function, contour integration and residue can be defined.

The book presents a detailed analysis of the hypercomplex numbers in 2, 3 and 4 dimensions, then presents the properties of hypercomplex numbers in 5 and 6 dimensions, and it continues with a detailed analysis of polar and planar hypercomplex numbers in n dimensions. The essence of this book is the interplay between the algebraic, the geometric and the analytic facets of the relations.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 2002

Количество страниц: 286

Добавлена в каталог: 13.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Poles and residues, planar fourcomplex      116
Poles and residues, planar n-complex      256
Poles and residues, polar 5-complex      163
Poles and residues, polar 6-complex      179
Poles and residues, polar fourcomplex      144
Poles and residues, polar n-complex      227
Poles and residues, tricomplex      45
Polynomial, canonical variables, circular fourcomplex      75
Polynomial, canonical variables, hyperbolic fourcomplex      91
Polynomial, canonical variables, planar 6-complex      192
Polynomial, canonical variables, planar fourcomplex      119
Polynomial, canonical variables, planar n-complex      258
Polynomial, canonical variables, polar 5-complex      164
Polynomial, canonical variables, polar fourcomplex      146
Polynomial, canonical variables, polar n-complex      229
Polynomial, canonical variables, tricomplex      48
Polynomial, canonical variables, twocomplex      15
Polynomial, factorization, circular fourcomplex      76
Polynomial, factorization, hyperbolic fourcomplex      92
Polynomial, factorization, planar 6-cornplex      192
Polynomial, factorization, planar fourcomplex      120
Polynomial, factorization, planar n-complex      258
Polynomial, factorization, polar 5-complex      164
Polynomial, factorization, polar fourcomplex      146
Polynomial, factorization, polar n-complex      230
Polynomial, factorization, tricomplex      49
Polynomial, factorization, twocomplex      15
Polynomials, canonical variables, polar 6-complex      180
Polynomials, factorization, polar 6-complex      180
Power function, circular fourcomplex      64
Power function, hyperbolic fourcomplex      85 86
Power function, planar 6-cornplex      189
Power function, planar fourcomplex      109
Power function, planar n-complex      248
Power function, polar 5-complex      161
Power function, polar 6-complex      176
Power function, polar fourcomplex      137
Power function, polar n-complex      218
Power function, tricomplex      35
Power function, twocomplex      8
Power series, circular fourcomplex      66
Power series, hyperbolic fourcomplex      88
Power series, planar 6-complex      190
Power series, planar fourcomplex      111
Power series, planar n-complex      252
Power series, polar 5-complex      162
Power series, polar 6-complex      177
Power series, polar fourcomplex      140
Power series, polar n-complex      223
Power series, tricomplex      40
Power series, twocomplex      10
Product, circular fourcomplex      54
Product, hyperbolic fourcomplex      77
Product, planar 6-complex      182
Product, planar fourcomplex      93
Product, planar n-complex      234
Product, polar 5-complex      150
Product, polar 6-complex      168
Product, polar fourcomplex      121 122
Product, polar n-complex      199
Product, tricomplex      19
Product, twocomplex      2 3
Relations between partial derivatives, circular fourcomplex      69
Relations between partial derivatives, hyperbolic fourcomplex      89
Relations between partial derivatives, planar 6-complex      191
Relations between partial derivatives, planar fourcomplex      113
Relations between partial derivatives, planar n-complex      254
Relations between partial derivatives, polar 5-complex      163
Relations between partial derivatives, polar 6-complex      178
Relations between partial derivatives, polar fourcomplex      141
Relations between partial derivatives, polar n-complex      225
Relations between partial derivatives, tricomplex      44
Relations between partial derivatives, twocomplex      14
Relations between second-order derivitives, circular fourcomplex      69
Relations between second-order derivitives, hyperbolic fourcomplex      90
Relations between second-order derivitives, planar 6-complex      191
Relations between second-order derivitives, planar fourcomplex      113
Relations between second-order derivitives, planar n-complex      254
Relations between second-order derivitives, polar 5-complex      163
Relations between second-order derivitives, polar 6-complex      179
Relations between second-order derivitives, polar fourcomplex      141
Relations between second-order derivitives, polar n-complex      225
Relations between second-order derivitives, tricomplex      44
Relations between second-order derivitives, twocomplex      14
Representation by irreducible matrices      50
Representation by irreducible matrices, circular fourcomplex      76
Representation by irreducible matrices, hyperbolic fourcomplex      93
Representation by irreducible matrices, planar 6-complex      193
Representation by irreducible matrices, planar fourcomplex      121
Representation by irreducible matrices, planar n-complex      259
Representation by irreducible matrices, polar 5-complex      165
Representation by irreducible matrices, polar 6-complex      181
Representation by irreducible matrices, polar fourcomplex      147
Representation by irreducible matrices, polar n-complex      232
Representation by irreducible matrices, twocomplex      16
Roots, circular fourcomplex      73
Roots, planar fourcomplex      118
Rules for derivation and integration      13
Series, circular fourcomplex      65
Series, hyperbolic fourcomplex      87
Series, planar fourcomplex      110
Series, planar n-complex      251
Series, polar fourcomplex      139
Series, polar n-complex      222
Series, tricomplex      38
Series, twocomplex      10
Sum, circular fourcomplex      54
Sum, hyperbolic fourcomplex      77
Sum, planar 6-complex      182
Sum, planar fourcomplex      93
Sum, planar n-complex      234
Sum, polar 5-complex      150
Sum, polar 6-complex      168
Sum, polar fourcomplex      121 122
Sum, polar n-complex      198
Sum, tricomplex      19
Sum, twocomplex      2 3
Transformation of variables, circular fourcomplex      58 67
Transformation of variables, hyperbolic fourcomplex      80
Transformation of variables, planar 6-complex      184
Transformation of variables, planar fourcomplex      97 108 112
Transformation of variables, planar n-complex      238
Transformation of variables, polar 5-complex      153
Transformation of variables, polar 6-complex      171
Transformation of variables, polar fourcomplex      124 125 134 136
Transformation of variables, polar n-complex      206
Transformation of variables, tricomplex      23 25 42
Transformation of variables, twocomplex      5
Trigonometric form, circular fourcomplex      63
Trigonometric form, expression      7
Trigonometric form, hyperbolic fourcomplex      84
Trigonometric form, planar 6-complex      189
Trigonometric form, planar fourcomplex      107
Trigonometric form, planar n-complex      246
Trigonometric form, polar 5-complex      160
Trigonometric form, polar 6-complex      176
Trigonometric form, polar fourcomplex      135
Trigonometric form, polar n-complex      216
Trigonometric form, tricomplex      34
Trigonometric functions, expressions, circular fourcomplex      64
Trigonometric functions, expressions, hyperbolic fourcomplex      86
Trigonometric functions, expressions, planar 6-complex      190
Trigonometric functions, expressions, planar fourcomplex      109
Trigonometric functions, expressions, planar n-complex      249 250
Trigonometric functions, expressions, polar 5-complex      161
Trigonometric functions, expressions, polar 6-complex      177
Trigonometric functions, expressions, polar fourcomplex      138
Trigonometric functions, expressions, polar n-complex      219 221
Trigonometric functions, expressions, tricomplex      36
Trigonometric functions, expressions, twocomplex      9
Trigonometric functions, hypercomplex, addition theorems      9
Trigonometric functions, hypercomplex, definitions      9
Trisector line      21
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