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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
Amplitude, circular fourcomplex      55
Amplitude, hyperbolic fourcomplex      79
Amplitude, planar 6-complex      184
Amplitude, planar fourcomplex      95
Amplitude, planar n-complex      235
Amplitude, polar 5-complex      153
Amplitude, polar 6-complex      171
Amplitude, polar n-complex      200
Amplitude, tricomplex      25
Amplitude, twocomplex      4
Analytic function, hypercomplex, definition      12
Analytic function, hypercomplex, expansion in series      12
Analytic function, hypercomplex, power series      12
Azimuthal angle, polar fourcomplex      125
Azimuthal angle, tricomplex      21
Azimuthal angles, circular fourcomplex      56
Azimuthal angles, planar 6-complex      184
Azimuthal angles, planar fourcomplex      96
Azimuthal angles, planar n-complex      238
Azimuthal angles, polar 5-complex      152
Azimuthal angles, polar 6-complex      170
Azimuthal angles, polar n-complex      204
Canonical base, circular fourcomplex      67
Canonical base, hyperbolic fourcomplex      81
Canonical base, planar 6-complex      188
Canonical base, planar fourcomplex      112
Canonical base, planar n-complex      245
Canonical base, polar 5-complex      159
Canonical base, polar 6-complex      175
Canonical base, polar fourcomplex      127
Canonical base, polar n-complex      212
Canonical base, tricomplex      40
Canonical base, twocomplex      5
Canonical form, circular fourcomplex      67
Canonical form, hyperbolic fourcomplex      81
Canonical form, planar 6-complex      189
Canonical form, planar fourcomplex      111
Canonical form, planar n-complex      245
Canonical form, polar 5-complex      160
Canonical form, polar 6-complex      175
Canonical form, polar fourcomplex      127
Canonical form, polar n-complex      213
Canonical form, twocomplex      5
Canonical variables, circular fourcomplex      56
Canonical variables, hyperbolic fourcomplex      79
Canonical variables, planar 6-complex      183
Canonical variables, planar fourcomplex      95
Canonical variables, planar n-complex      236
Canonical variables, polar 5-complex      151
Canonical variables, polar 6-complex      169
Canonical variables, polar fourcomplex      125
Canonical variables, polar n-complex      201
Canonical variables, tricomplex      40
Canonical variables, twocomplex      3
Complex units, circular fourcomplex      54
Complex units, hyperbolic fourcomplex      77
Complex units, planar 6-complex      181
Complex units, planar fourcomplex      93
Complex units, planar n-complex      233
Complex units, polar 5-complex      150
Complex units, polar 6-complex      168
Complex units, polar fourcomplex      122
Complex units, polar n-complex      198
Complex units, powers of circular fourcomplex      59
Complex units, powers of hyperbolic fourcomplex      83
Complex units, powers of planar fourcomplex      100
Complex units, powers of planar n-complex      240
Complex units, powers of polar fourcomplex      128
Complex units, powers of polar n-complex      208
Complex units, powers of tricomplex      27
Complex units, powers of twocomplex      6
Complex units, tricomplex      19
Complex units, twocomplex      2
Convergence of power series, circular fourcomplex      66
Convergence of power series, hyperbolic fourcomplex      88
Convergence of power series, planar 6-complex      190
Convergence of power series, planar fourcomplex      111
Convergence of power series, planar n-complex      252
Convergence of power series, polar 5-complex      162
Convergence of power series, polar 6-complex      177
Convergence of power series, polar fourcomplex      140
Convergence of power series, polar n-complex      223
Convergence of power series, tricomplex      40
Convergence of power series, twocomplex      11
Convergence, region of circular fourcomplex      68
Convergence, region of hyperbolic fourcomplex      89
Convergence, region of planar 6-complex      191
Convergence, region of planar fourcomplex      112
Convergence, region of planar n-complex      253
Convergence, region of polar 5-complex      162
Convergence, region of polar 6-complex      178
Convergence, region of polar fourcomplex      141
Convergence, region of polar n-complex      224
Convergence, region of tricomplex      42
Convergence, region of twocomplex      11
Cosexponential function, polar 5-complex, definition      154
Cosexponential function, polar four-complex, definitions      128
Cosexponential function, polar n-complex, definition      208
Cosexponential functions, planar 6-complex, addition theorems      186
Cosexponential functions, planar 6-complex, definition      185
Cosexponential functions, planar 6-complex, differential equations      188
Cosexponential functions, planar 6-complex, expressions      185
Cosexponential functions, planar 6-complex, parity      185
Cosexponential functions, planar four-complex, addition theorems      100
Cosexponential functions, planar four-complex, definitions      100
Cosexponential functions, planar four-complex, differential equations      103
Cosexponential functions, planar four-complex, expressions      103
Cosexponential functions, planar four-complex, parity      100
Cosexponential functions, planar n-complex, addition theorems      243
Cosexponential functions, planar n-complex, definition      241
Cosexponential functions, planar n-complex, differential equations      244
Cosexponential functions, planar n-complex, expressions      241
Cosexponential functions, planar n-complex, parity      241
Cosexponential functions, polar 5-complex, addition theorems      159
Cosexponential functions, polar 5-complex, differential equations      159
Cosexponential functions, polar 5-complex, expressions      154 156
Cosexponential functions, polar 6-complex, addition theorems      173
Cosexponential functions, polar 6-complex, definitions      172
Cosexponential functions, polar 6-complex, differential equations      175
Cosexponential functions, polar 6-complex, expressions      172
Cosexponential functions, polar 6-complex, parity      172
Cosexponential functions, polar four-complex, addition theorems      129
Cosexponential functions, polar four-complex, differential equations      133
Cosexponential functions, polar four-complex, expressions      131
Cosexponential functions, polar four-complex, parity      129
Cosexponential functions, polar n-complex, addition theorems      210
Cosexponential functions, polar n-complex, differential equations      211
Cosexponential functions, polar n-complex, expressions      209
Cosexponential functions, polar n-complex, parity      208
Cosexponential functions, tricomplex, addition theorems      28
Cosexponential functions, tricomplex, definitions      28
Cosexponential functions, tricomplex, differential equations      31
Cosexponential functions, tricomplex, expressions      30
Derivative, hypercomplex of power function      12
Derivative, hypercomplex, definition      12
Derivative, independence of direction, fourcomplex      68
Derivative, independence of direction, planar n-complex      253
Derivative, independence of direction, polar n-complex      224
Derivative, independence of direction, tricomplex      43
Derivative, independence of direction, twocomplex      13
Distance, canonical variables, polar fourcomplex      125
Distance, circular fourcomplex      56
Distance, hyperbolic fourcomplex      80
Distance, planar 6-complex      183
Distance, planar fourcomplex      95
Distance, planar n-complex      236
Distance, polar 5-complex      152
Distance, polar 6-complex      170
Distance, polar fourcomplex      124
Distance, polar n-complex      202
Distance, tricomplex      23
Distance, twocomplex      4
Divisors of zero, hyperbolic fourcomplex      79
Divisors of zero, planar n-complex      240
Divisors of zero, polar n-complex      208
Divisors of zero, tricomplex      20
Divisors of zero, twocomplex      4
Exponential form, circular fourcomplex      62
Exponential form, hyperbolic fourcomplex      84
Exponential form, planar 6-complex      189
Exponential form, planar fourcomplex      107
Exponential form, planar n-complex      246
Exponential form, polar 5-complex      160
Exponential form, polar 6-complex      176
Exponential form, polar fourcomplex      134
Exponential form, polar n-complex      215
Exponential form, tricomplex      34
Exponential form, twocomplex      7
Exponential function, hypercomplex, addition theorem      6
Exponential function, hypercomplex, definition      6
Exponential, expression, twocomplex      7
Exponential, expressions, circular fourcomplex      60
Exponential, expressions, hyperbolic fourcomplex      83
Exponential, expressions, planar 6-complex      185 190
Exponential, expressions, planar fourcomplex      100
Exponential, expressions, planar n-complex      241
Exponential, expressions, polar 5-complex      154 161
Exponential, expressions, polar 6-complex      172 177
Exponential, expressions, polar fourcomplex      128
Exponential, expressions, polar n-complex      208 220
Exponential, expressions, tricomplex      28
Functions, real components, circular fourcomplex      68
Functions, real components, planar 6-complex      191
Functions, real components, planar n-complex      253
Functions, real components, polar 5-complex      163
Functions, real components, polar n-complex      224
Functions, real components, tricomplex      42
Functions, real components, twocomplex      13
Hyperbolic functions, expressions, circular fourcomplex      65
Hyperbolic functions, expressions, hyperbolic fourcomplex      86
Hyperbolic functions, expressions, planar 6-complex      190
Hyperbolic functions, expressions, planar fourcomplex      109
Hyperbolic functions, expressions, planar n-complex      250 251
Hyperbolic functions, expressions, polar 5-complex      161
Hyperbolic functions, expressions, polar 6-complex      177
Hyperbolic functions, expressions, polar fourcomplex      138
Hyperbolic functions, expressions, polar n-complex      220 221
Hyperbolic functions, expressions, tricomplex      37
Hyperbolic functions, expressions, twocomplex      9
Hyperbolic functions, liypercomplex, addition theorems      9
Hyperbolic functions, liypercomplex, definitions      9
Integrals, path, circular fourcomplex      70
Integrals, path, hyperbolic fourcomplex      90
Integrals, path, planar 6-complex      192
Integrals, path, planar fourcomplex      114
Integrals, path, planar n-complex      255
Integrals, path, polar 5-complex      163
Integrals, path, polar 6-complex      179
Integrals, path, polar fourcomplex      142
Integrals, path, polar n-complex      226
Integrals, path, tricomplex      45
Integrals, path, twocomplex      14
Inverse, circular fourcomplex      55
Inverse, determinant, hyperbolic fourcomplex      78
Inverse, determinant, planar fourcomplex      95
Inverse, determinant, planar n-complex      235 236
Inverse, determinant, polar fourcomplex      123
Inverse, determinant, polar n-complex      200 201
Inverse, determinant, tricomplex      20 26
Inverse, determinant, twocomplex      3
Inverse, hyperbolic fourcomplex      78
Inverse, planar fourcomplex      94
Inverse, planar n-complex      235
Inverse, polar fourcomplex      122
Inverse, polar n-complex      200
Inverse, tricomplex      20
Inverse, twocomplex      3
Logarithm, circular fourcomplex      64
Logarithm, hyperbolic fourcomplex      85
Logarithm, planar 6-complex      189
Logarithm, planar fourcomplex      109
Logarithm, planar n-complex      247
Logarithm, polar 5-complex      161
Logarithm, polar 6-complex      176
Logarithm, polar fourcomplex      137
Logarithm, polar n-complex      217 218
Logarithm, tricomplex      35
Logarithm, twocomplex      8
Matrix representation, circular fourcomplex      59
Matrix representation, hyperbolic fourcomplex      82
Matrix representation, planar 6-complex      184
Matrix representation, planar fourcomplex      99
Matrix representation, planar n-complex      240
Matrix representation, polar 5-complex      153
Matrix representation, polar 6-complex      171
Matrix representation, polar fourcomplex      128
Matrix representation, polar n-complex      207
Matrix representation, tricomplex      26
Matrix representation, twocomplex      6
Modulus, canonical variables, circular fourcomplex      67
Modulus, canonical variables, hyperbolic fourcomplex      82
Modulus, canonical variables, planar 6-complex      184
Modulus, canonical variables, planar fourcomplex      112
Modulus, canonical variables, planar n-complex      237
Modulus, canonical variables, polar 6-complex      171
Modulus, canonical variables, polar n-complex      203
Modulus, canonical variables, tricomplex      41
Modulus, canonical variables, twocomplex      4
Modulus, definition, circular fourcomplex      65
Modulus, definition, hyperbolic fourcomplex      87
Modulus, definition, planar fourcomplex      110
Modulus, definition, planar n-complex      236
Modulus, definition, polar fourcomplex      139
Modulus, definition, polar n-complex      202
Modulus, definition, tricomplex      39
Modulus, definition, twocomplex      10
Modulus, hyperbolic fourcomplex      80
Modulus, inequalities, circular fourcomplex      66
Modulus, inequalities, hyperbolic fourcomplex      87
Modulus, inequalities, planar 6-complex      190
Modulus, inequalities, planar fourcomplex      110
Modulus, inequalities, planar n-complex      251
Modulus, inequalities, polar 5-complex      152 162
Modulus, inequalities, polar 6-complex      177
Modulus, inequalities, polar fourcomplex      139
Modulus, inequalities, polar n-complex      222
Modulus, inequalities, tricomplex      39
Modulus, inequalities, twocomplex      10
Nodal hyperplanes, circular fourcomplex      56
Nodal hyperplanes, planar fourcomplex      95
Nodal hyperplanes, polar fourcomplex      123
Nodal hypersurfaces, planar n-complex      236
Nodal hypersurfaces, polar n-complex      201
Nodal line, tricomplex      20
Nodal lines, twocomplex      4
Nodal plane, tricomplex      20
Planar angle, circular fourcomplex      56
Planar angle, planar fourcomplex      96
Planar angle, polar 5-complex      152
Planar angle, polar 6-complex      170
Planar angles, planar 6-complex      184
Planar angles, planar n-complex      238
Planar angles, polar n-complex      204
Polar angle, polar 5-complex      152
Polar angle, tricomplex      23
Polar angles, polar 6-complex      171
Polar angles, polar fourcomplex      125
Polar angles, polar n-complex      204
Poles and residues, circular fourcomplex      71
Poles and residues, planar 6-complex      192
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