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| Авторизация |
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| Kurosh A. — Higher Algebra |
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| Предметный указатель |
Rank theorem 72 74
Rational fractions 156 298
Rational fractions, field of 297ff
Rational fractions, in lowest terms 156
Rational fractions, proper 156
Rational fractions, simplified 156
Rational numbers 107
Rational numbers, field of 341
Rational roots of integral polynomials 345ff
Real linear spaces 178
Real numbers 107
Real part 112
Reals, axis of 112
Rectangular matrices 70
Rectangular matrices, multiplication of 97
Reduced system 86
Reducibility of polynomials over the field of rationale 341ff
Reducible (of a polynomial) 281 306
Reduction of a matrix to diagonal form 203
Reduction of a matrix to Jordan normal form 375
Reduction of quadratic forms to canonical form 161ff
Reduction of quadratic forms to principal axes 168 219ff
Regula Falsi 251
Relation, equivalence 356
Relatively prime polynomials 133
Relatively prime polynomials, theorems on 137
Relatively prime system of polynomials 138
Remainder of polynomials (in division) 131
Resultant 326 327 330
Right decomposition 392
Right inverse matrix 94
Right-identity 384
Right-inverse 384
Ring(s) 10 260ff
Ring, commutative 267
Ring, concept of 257
Ring, definition of 262
Ring, examples of 262
Ring, finite 268
Ring, nonassociative 267
Ring, noncommutative 266
Ring, number 257 258 259
Ring, of functions 262
Ring, of polynomials 279 304
Ring, theory of 10 13
Root(s),  -fold 141
Root(s), approximation of 250ff
Root(s), bounds of 232ff
Root(s), characteristic 199ff 216
Root(s), matrix 378
Root(s), multiple 141
Root(s), of complex numbers 120ff 122 123
Root(s), of polynomials 139ff 378
Root(s), of unity 124ff
Root(s), of unity, primitive  th 125
Root(s), primitive 391
Root(s), rational (of integral polynomials) 345ff
Root(s), simple 141
Root(s), theorem on the existence of a 290
Root(s), theorems on the number of real 244
Ruffini, P. 12
Scalar matrices 102
Scalar product of vectors 204
Scalar, multiplication 204
Schmidt, O.Yu 14 415
Schreier, O. 414
Self-adjoint transformation 215
Semidefinite quadratic forms 177
Semigroups, theory of 13
Sequence, Sturm’s 239
Set, countable 352
Set, denumerable 352
Set, noncountable 352
Shapiro, G.M. 414
Shatunovsky, S.O. 43
Shilov, G.E. 414
Signature of a form 172
Similar matrices 192ff 200
Similar square matrices 192
Similarity of matrices, fundamental theorem on 367
Simple factor 284
Simple root 141
Simple spectrum 202 203
Simplified rational fraction 156
Single factor 284
Singular linear transformation 93
Singular square matrix 93
Skew-symmetric determinant 42
Solvability of equations by radicals 12
Sominsky, I.S. 414
Space(s), complex linear 181 202
Space(s), Euclidean 204 (see also Euclidean space)
Space(s), finite-dimensional 182
Space(s), four-dimensional 7
Space(s), infinite-dimensional 9
Space(s), linear 7 178ff
Space(s), linear, -dimensional 185
Space(s), linear, finite-dimensional 183
Space(s), linear, infinite-dimensional 481
Space(s), multidimensional 7
Space(s), null 197
Space(s), of functions 185
Space(s), of sequences 185
Space(s), real affine 178
Space(s), real linear 478 481
Space(s), real linear, isomorphic 181
Space(s), real vector 178
Space(s), unitary 209
Space(s), unitary, finite-dimensional 210
Space(s), vector 7 (see also Vector spaces)
Space(s), vector, theory of 9
Spectrum of a linear transformation 200
Spectrum, simple 202 203
Sperner, E. 414
Splitting field 416
Square matrix 93
Sturm method 238
Sturm sequence 239
Sturm theorem 238ff
Subfields 271ff
Subgroup(s) 388ff
Subgroup(s), cyclic 389
Subgroup(s), generated by subgroups 401
Subgroup(s), invariant 394
Subgroup(s), primary 407
Subgroup(s), unit 389
Submatrix, Jordan 371
Subspace(s), linear 195ff 202
Subspace(s), linear, generation of 196
Subspace(s), zero 195
Substitution, linear 87
Subtraction 261
Successive elimination of unknowns, method of 15 17
Sum(s) of classes 293 300
Sum(s) of polynomials 304
Sum(s), direct 400 403
Sum(s), power 322
Summands of a decomposition 100
Sushkevich, A.K. 414 415
Sylow 13
Sylvester, J.J. 43
Symmetric functions 342
Symmetric polynomial in two systems of unknowns 324
Symmetric polynomials 342ff 349ff
Symmetric polynomials, elementary 343
| Symmetric polynomials, fundamental theorem of 344 346 349
Symmetric rational fractions 324
Symmetric transformations 245
System(s) of Cayley numbers 444
System(s) of complex numbers 407ff
System(s) of complex numbers, definition of 440
System(s) of homogeneous linear equations 82
System(s) of homogeneous linear equations, solutions of 83
System(s) of integers 407
System(s) of linear equations 76
System(s) of linear equations, , determinate 46
System(s) of linear equations, , general theory of 59ff
System(s) of linear equations, , indeterminate 46
System(s) of linear equations, arbitrary, solution of 79
System(s) of linear equations, consistent 46
System(s) of linear equations, inconsistent 46
System(s) of nonhomogeneous equations 83
System(s) of quaternions 444
System(s) of rational numbers 107
System(s) of real numbers 107
System(s) of solutions, fundamental 84
System(s) of vectors, equivalent 67
System(s) of vectors, linearly dependent 63 64
System(s) of vectors, linearly independent 63
System(s) of vectors, maximal linearly independent 65 68
System(s) orthogonal (of vectors) 206
System(s) reduced 86
Tartaglia, N. 12
Taylor’s Formula 145
Tensor algebra 9
Term, degree of 303
Term, highest, of a polynomial 311
Theorem(s) see Lemma
Theorem, binomial 120
Theorem, Budan — Fourier 246 249
Theorem, Cayley — Hamilton 380 381
Theorem, Descartes 247 249 348
Theorem, fundamental (of higher algebra) 143
Theorem, fundamental (of the algebra of complex numbers) 142ff
Theorem, fundamental (of the algebra of complex numbers), alternative proof of 337
Theorem, fundamental (on finite Abelian groups) 406
Theorem, fundamental, corollaries to 151
Theorem, fundamental, on symmetric polynomials 314 316 319
Theorem, fundamental, on the similarity of Theorem, matrices 367
Theorem, Kronecker — Capelli 77 78 81
Theorem, Lagrange’s 393 557
Theorem, Laplace’s 50 51
Theorem, multiplication (for determinants) 91 93
Theorem, Newton’s binomial 120
Theorem, on homomorphisms 398
Theorem, on relatively prime polynomials 137
Theorem, on the existence of a root 290
Theorem, on the existence of roots, fundamental 12
Theorem, on the number of real roots 244
Theorem, principal-axis 219 220
Theorem, rank 72 74
Theorem, Sturm’s 238ff
Theorem, unique factorization 308
Theorem, Weierstrass 150 211
Theory of algebras 13
Topological algebra 11 13
Topological properties of real and complex numbers 143
Transcendence of  349
Transcendence of  259
Transcendental numbers 349 353 354
Transcendental over a field 279 305
Transform of an element 395
Transformation(s), affine 214
Transformation(s), elementary 74 102
Transformation(s), elementary, of a matrix 355
Transformation(s), identity 189 195 214
Transformation(s), inverse 199 279
Transformation(s), linear 87 89 188;
Transformation(s), linear, nonsingular 93
Transformation(s), linear, operations on 193
Transformation(s), linear, singular 93
Transformation(s), nonsingular 211
Transformation(s), nullity of 197 198
Transformation(s), of vector coordinates 186
Transformation(s), orthogonal 210ff
Transformation(s), orthogonal, of Euclidean space 212
Transformation(s), range of values of 197
Transformation(s), self-adjoint 215
Transformation(s), symmetric 215
Transformation(s), zero 189 195 215
Transpose of a determinant, taking 38
Transpose of a matrix 162
Transpose operation 38
Transposition 34
Trigonometric form (of complex numbers) 114
Unimodular  -matrices 362ff
Unique decomposition of a proper rational fraction 159
Unique decomposition of a proper rational fraction, example of 160
Unique factorization theorem 308
Unit element 269
Unit element of a group 383 385
Unit matrix 16 93 195 211
Unit subgroup 389
Unit vectors 64 185
Unit, class 294 301
Unit, imaginary 112
Unitary space(s) 210
Unitary space(s), finite-dimensional 210
Unity 269
Unity, divisor of 285
Unity, primitive th roots of 125
Unity, roots of 124
Universal algebras 11
Unknowns, free 79
Value of a polynomial 377 381
Van der Waerden, B.L. 415
Vandermonde determinant 49 329 336
Vector space(s) 9 178
Vector space(s), -dimensional 59 60 62
Vector space(s), multidimensional 59
Vector space(s), theory of 9
Vector(s) 178
Vector(s), -dimensional 60
Vector(s),  -dimensional 60
Vector(s), examples of 60 81
Vector(s), multiplication of by a scalar 61
Vector(s), normalized 207
Vector(s), opposite 61
Vector(s), unit 64 185
Vector(s), zero 61
Vectorial angle 113
Vieta (Vi te) F. 12
Vieta’s formulas 154 217 296 313
Vinogradov, S.P. 414
Voronoi, G.F. 13
Waerden, van der, B.L. 415
Weierstrass theorem 150
Weight of a term 320 332
Weyl, H. 415
Zero 109
Zero class 294 300
Zero element 180 264
Zero matrix 100 195
Zero multiple 265
Zero power 389
Zero subspace 195
Zero transformation 189 195 215
Zero vector 60
Zero, the number 61
Zolotarev, E.I. 13
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