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Vein R., Dale P. — Determinants and their applications in mathematical physics
Vein R., Dale P. — Determinants and their applications in mathematical physics

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Название: Determinants and their applications in mathematical physics

Авторы: Vein R., Dale P.

Аннотация:

This book is unique. It contains a detailed account of all important relations in the analytic theory of determinants from the classical work of Laplace, Cauchy and Jacobi in the 18th and 19th centuries to the most recent 20th century developments. Several contributions have never been published before. The first five chapters are purely mathematical in nature and make extensive use of the column vector notation and scaled cofactors. They contain a number of important relations involving derivatives which prove beyond a doubt that the theory of determinants has emerged from the confines of classical algebra into the brighter world of analysis. The whole of Chapter 4 is devoted to particular determinants including alternants, Wronskians and Hankelians. The contents of Chapter 5 include the Cusick and Matsuno identities. Chapter 6 is devoted to the verifications of the known determinantal solutions of several nonlinear equations which arise in three branches of mathematical physics, namely lattice, soliton and relativity theory. They include the KdV, Toda and Einstein equations. The solutions are verified by applying theorems established in earlier chapters and in the extensive appendix. The book ends with an extensive bibliography and an index. Mathematicians, physicists and engineers who wish to become acquainted with modern developments in the analytic theory of determinants will find the book indispensable.


Язык: en

Рубрика: Математика/Алгебра/Линейная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 376

Добавлена в каталог: 19.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Ablowitz and Segur      237
Adjoint and adjugate      36
Adjunct functions      102
Algebraic computing      226
Backlund transformations      337
Beckenback      153 157
Bessel functions      336
Brand      169
Browne and Nillsen      169
Burchnall      153
Burgmeier      97
Carlson      154
Cauchy, v      48 154 336
Caudrey      223
Cayley      v
Chalkley      152
Chaundy      154
Cofactors, alien      12 22
Cofactors, derivatives of      23 35 100 118
Cofactors, double-sum relations      34 112
Cofactors, expansion      20
Cofactors, first      3 12
Cofactors, operations on      24
Cofactors, second and higher      19
Cofactors, simple and scaled      23
Column vectors      7
Computers and computing      226
Continued fraction      201
Cordoneanu      104
Cramer      13 24
Cusick      178 186
Cyclic dislocations      16
Cyclic permutations      23
Dale      236 241 246 318
DAS      153
Derivative of cofactors      23 35 100 118
Derivative of determinants      15
Derivative with respect to an element      12 20 24 27 43 88 111 185 192 268
Determinantal solutions      235
Determinants containing blocks of zero elements      30
Determinants whose elements are Appell polynomials      115 119
Determinants whose elements are binomial and factorial numbers      142
Determinants whose elements are differences      106
Determinants whose elements are other determinants      227 230
Determinants whose elements are prime numbers      232
Determinants, adjoint or adjugate      36
Determinants, arbitrary      102
Determinants, basic properties      8
Determinants, bordered      46 48 67 129 181 232
Determinants, Casorati      169 303
Determinants, Cauchy expansion      36 48
Determinants, centrosymmetric      85
Determinants, circulants      79
Determinants, continuants      201
Determinants, definition      3
Determinants, derivative      15
Determinants, equivalent      212
Determinants, expansion, Cauchy      46
Determinants, expansion, Laplace      25
Determinants, expansion, simple      13
Determinants, factors, centrosymmetric      85
Determinants, factors, circulants      79
Determinants, factors, skew-symmetric      67
Determinants, factors, symmetric Toeplitz      87
Determinants, Fredholm      240
Determinants, Hankel      104
Determinants, Hessenberg      90
Determinants, Hilbert      123
Determinants, hybrid      37 55
Determinants, Laplace expansion      25
Determinants, Matsuno      192
Determinants, nondistinct      211
Determinants, notation      vi
Determinants, persymmetric      105
Determinants, product of two, three      5 33 34
Determinants, recurrent      91
Determinants, simple expansion      13
Determinants, skew-centrosymmetric      90
Determinants, skew-symmetric      65
Determinants, symmetric      64
Determinants, symmetric Toeplitz      87
Determinants, Toeplitz      87
Determinants, Turanian      109
Determinants, value identically 1      83
Determinants, value identically 9      15 98 260 262
Determinants, Vandermonde      52
Determinants, Wronskian      271 280
Determinants, Yamazaki — Hori      232
Differences      328
Double-sum relations      34 112
Ehlers      339
Equations, Appell      314
Equations, Benjamin — Ono      241 281
Equations, Dale      236 246
Equations, Einstein      241 287
Equations, Ernst      241 245 302
Equations, Kadomtsev — Petviashvili      240 277
Equations, Kay — Moses      237 249
Equations, Korteweg — de Vries      239 263
Equations, Matsukidaira — Satsuma      239 258
Equations, Milne — Thomson      256
Equations, Toda      237 252
Ernst      241 287 302
Euler’s theorem on homogeneous functions      330
Expansion, Cauchy      46
Expansion, Laplace      25
Expansion, of cofactors      20
Factors, centrosymmetric      85
Factors, circulants      79
Factors, skew-symmetric      67
Factors, symmetric Toeplitz      87
Fiedler      214
Freeman      240
Frost and Sackfield      173
Generalized geometric series      172 323
Generalized hyperbolic functions      81
Generating functions      321 322
Geronimus      153
Gradner, Greene, Kruskal, and Miura      240
Grassmann      1 25
Gravitational fields      235
hilbert      123 241
Hildebrand      318
Hirota      169 240 244 295
homogeneous functions      108 330
Hori      116 129 135 244
Identities, Cauchy      36
Identities, Cusick      178
Identities, double-sum      112
Identities, equivalent determinants      212
Identities, Hirota operator      221
Identities, hybrid determinant      37 55
Identities, Jacobi and variants      38
Identities, matrix      165 233
Identities, Matsuno      187
Identities, multiple-sum      311
Identities, Vandermondian      60 63
Integral equations, Fredholm      240
Integral equations, Gelfand, Levitan, and Marchenko      236
Inverceanu      84
jacobi      v 38
Kac      237
Kajiwara      169 238
Karlin      109 153
Kaufman      84
Kerr      244
Kronecker delta function      304
Kyriakopoulos      244
Lamb      240
Langmuir waves      238
Laplace      v
Laplace expansion      25
Lattice theory      235
Laurent series      335
Lawden      153 157 165
Leibniz      v 221
Littlewood      187
Liu      169
l’Hopital      52
Matsuno      187 192 241 281
Milne–Thomson      169 238
Mina      99
Minors, complementary      19
Minors, first      12
Minors, rejecter and retainer      18
Minors, second and higher      19
Muir and Metzler      v 78 177 341
Nakamura, A.      240
Nakamura, Y.      243 245
Neugebauer      244
Nimmo      240
Numbers, binomial and factorial      212
Numbers, complex      79 256
Numbers, Eulerian      325
Numbers, prime      232
Numbers, Stirling      217 306 324
Numbers, v-      137
Ohta      169 246
Operations, row and column      10
Operators, associated with cofactors      24
Operators, Hirota      221
Pandres      174
permutations      307
Pfaffians      73
Pipes      84
plasma      238
Polynomials, Appell      314
Polynomials, characteristic      94
Polynomials, Euler and Eulerian      157 323
Polynomials, Hermite      322
Polynomials, homogeneous      112
Polynomials, identical      212
Polynomials, Laguerre      153 321
Polynomials, Lawden      157
Polynomials, Legendre      154 322
Polynomials, orthogonal      153 321
Polynomials, symmetric      54 326
Poppe      240
Product of two, three determinants      5 33 35
Reciprocal differences      238
Reciprocal power series      92
Recurrence relations      264 265 321 322
Rejecter and retainer minors      18
Relativity theory      235 241
Rodrigues      127 154 174 321 322 323
Rosler      174
Row vectors      7
Rujisenaars      245
Sasa      244 295
Sato      244
Satsuma      170 239 244 295
Scaled cofactors      23
Schmidt      84
Schrodinger      237
Seidel      153
Servomechanisms      325
Soliton theory      235
Stein      174
Sum formulas for elements and cofactors      13
Sum formulas for Hankelians      108
Sum formulas, Laplace      32
Szego      153
Taylor      221 318
Toda      237 252
Tomimatsu      244
Trahan      18
Van Moerbeke      237
Vandermonde      v
Vectors, row and column      7
Vein      84 244 316 318
Wadati      240
Waves      235 237
Yahya      174
Yamazaki, M.      116 129 135 232
Yamazaki, S.      238
Yebbou      178
z-transform      325
Zacharov, Musher, and Rubenchick      238
Zeitlin      324
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