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| Авторизация |
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| Kurosh A. — Higher Algebra |
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| Предметный указатель |
Matrices,  -matrices, equivalent 356
Matrices, -matrices, unimodular 362ff
Matrices, diagonal 371
Matrices, fundamental theorem on the similarity of 367
Matrices, inverse 93ff
Matrices, Jordan 370
Matrices, noncommutative 90
Matrices, numerical 355
Matrices, of a linear transformation in different bases, relationship between 191
Matrices, orthogonal 210ff 214
Matrices, polynomial 355
Matrices, product of 124
Matrices, rectangular 70
Matrices, rectangular, multiplication of 97
Matrices, scalar 102
Matrices, similar 192 200
Matrices, similarity of, fundamental theorem on 367
Matrices, square, similar 192
Matrices, theory of 8
Matrix 16 (see also Matrices)
Matrix addition 99
Matrix multiplication 87ff 89
Matrix polynomials 365
Matrix root of a polynomial 378
Matrix, adjoint of 94
Matrix, augmented 21
Matrix, change-оf-basis 186
Matrix, characteristic 199
Matrix, definition of 23
Matrix, diagonalization of 203
Matrix, elementary 363
Matrix, elementary divisors of 376
Matrix, elementary transformations of 355
Matrix, identity 93
Matrix, Jordan (of order  ) 370
Matrix, left-inverse 94
Matrix, multiplication of by a scalar 99 100
Matrix, normal form of 355ff
Matrix, of a quadratic form 162
Matrix, reduction of to diagonal form 75 203
Matrix, reduction of to Jordan normal form 375
Matrix, right-inverse 94
Matrix, square 93
Matrix, square, nonsingular 93
Matrix, square, of order 16
Matrix, square, singular 93
Matrix, transformations of, elementary 355
Matrix, unit 16 93 195 211
Matrix, zero 100 195
Maximal linearly independent system of vectors 65 68
Method, alphabetical 310
Method, Graeffe 256
Method, Horner 140 141
Method, iterative see Iterative procedure
Method, Newton’s 236 252 253
Method, of equalizing coefficients 23
Method, of false position 251
Method, of linear interpolation 251
Method, of Lobachevsky 256
Method, Sturm’s 238
Minimal polynomials 377ff
Minor(s) 43ff
Minor(s),  -th-order (of a matrix) 70
Minor(s), complementary 43
Minor(s), of order 43
Minor(s), principal (of a form) 175
Modulus 113
Modulus of a product of complex numbers 115
Modulus of a quotient of two complex numbers 116
Modulus of a sum 117
Molin, F.E. 13
Multidimensional space 7
Multidimensional vector spaces 59
Multiple factors 284 287
Multiple factors, isolation of 288
Multiple roots 141
Multiple zero 265
Multiple(s) of an element 389
Multiplication 261
Multiplication theorem for determinants 91 93
Multiplication, in a group 382
Multiplication, matrix, associativity of 96
Multiplication, noncommutativity of 90
Multiplication, of a matrix by a scalar 99 100
Multiplication, of classes 268
Multiplication, of rectangular matrices 97
Multiplication, of vectors by a scalar 61
Multiplication, scalar 204
Multiplicative group 386 391
Multiplicity of a root 141 152
Murnaghan, F.D. 415
Negative definite forms 177
Negative index of inertia 172
NeVton’s binomial theorem 120
Newton, Isaac 12
Newton’s Formulas 323
Newton’s method 236 252 253
Noether, E. 9
Noether, M. 13
Nonassociative rings 267
Noncommutable set 352
Noncommutative groups 387
Noncommutative matrices 90
Noncommutative ring 266
Noncommutativity of multiplication 90
Nonhomogeneous equations 83
Nonhomogeneous system 83
Nonsingular linear transformations 93 198
Nonsingular quadratic form 162
Nonsingular square matrix 93
Nonsingular transformation 211
Nonsingularity of a linear transformation 224
Norm of a number 286
Normal divisors 394 398
Normal form 169 170
Normal form of a matrix 355ff
Normalization of a vector 208
Normalized vector 207
Notation, additive 400
Null space of a linear transformation 197
Nullity of a transformation 197 198
Number fields 257 260 271
Number rings 257 258 259
Number(s), algebraic 349
Number(s), algebraic, conjugate 350
Number(s), algebraic, set of 350
Number, Cayley 111
Number, complex 107 110 112ff
Number, complex, raising to a power 120
Number, complex, taking roots of 120ff 122 123
Number, complex, taking the square root of 122
Number, conjugate 118
Number, conjugate complex 118
Number, hypercomplex 10
Number, irrational 105
Number, rational 105
Number, rational, field of 341
Number, real 105
Number, transcendental 349 353 354
Numerical matrices 355
Okunev, L.Ya 414 415
Omar Khayyam 12
Operation, algebraic 261
Operation, inverse 261
Opposite class 294
Opposite element 179
Order of a group 382
Orthogonal bases 207
orthogonal matrices 210ff 214
Orthogonal system (of vectors) 206
| Orthogonal transformation(s) 210ff
Orthogonal transformation(s) of Euclidean space 212
Orthogonalization process 206 207
Orthonormal bases 204 208
Orthonormal basis 208
Parity of permutations 34
Part, imaginary 112
Part, real 112
Partial fraction 157
Pedoe, D. 415
Permutation(s) 27ff
Permutation, cyclic 34
Permutation, decrement of 36
Permutation, definition of 28
Permutation, even 32
Permutation, identity 31
Permutation, inverse of 33
Permutation, multiplication of 32
Permutation, odd 32
Permutation, of degree (definition) 30 32
Permutation, parity of 34
Pi ( ), transcendence of 259
Plane, complex 112
Polar angle 113
Polynomial algebra of over an arbitrary field 276
Polynomial matrices 355
Polynomial(s) 156
Polynomial, th-degree 127
Polynomial, algebraic viewpoint of 127
Polynomial, alphabetic order of terms of 310 311
Polynomial, as a formal algebraic expression 127
Polynomial, characteristic (of a matrix) 200
Polynomial, cubic 127
Polynomial, cyclotomic 345
Polynomial, decomposition of 284
Polynomial, definition of 127
Polynomial, degree of 303
Polynomial, derivative of 141
Polynomial, dividend of 306
Polynomial, divisibility of 131 —133 305
Polynomial, divisor of 306
Polynomial, elementary divisors of a 376
Polynomial, equal 127 303
Polynomial, evaluating roots of 225ff
Polynomial, factorization of 284
Polynomial, factorization of, into irreducible factors 281
Polynomial, first-degree 127
Polynomial, from viewpoint of mathematical analysis 127
Polynomial, function-theoretic viewpoint of 127
Polynomial, greatest common divisor of 134
Polynomial, highest term of 311
Polynomial, homogeneous 306
Polynomial, identically equal 127 303
Polynomial, in several unknowns 303ff
Polynomial, integral, rational roots of 345ff
Polynomial, inverse 129
Polynomial, irreducible 281 306
Polynomial, is annihilated by a linear transformation 381
Polynomial, linear 127 139
Polynomial, matrix 365
Polynomial, minimal 377ff
Polynomial, of degree 127
Polynomial, of degree one 139
Polynomial, of degree zero 127 129
Polynomial, operations on 126ff
Polynomial, primitive 342
Polynomial, quadratic 127
Polynomial, quotient of 131
Polynomial, reducibility of over the field of rationale 341ff
Polynomial, reducible 281 306
Polynomial, relatively prime 133
Polynomial, relatively prime, theorems on 137
Polynomial, remainder in division of 131
Polynomial, ring of 279 304
Polynomial, roots of 139ff
Polynomial, sum of 304
Polynomial, symbols for 127
Polynomial, symmetric 312ff 319ff
Polynomial, symmetric, elementary 313
Polynomial, symmetric, fundamental theorem on 314 316 319
Polynomial, symmetric, in two systems of unknowns 324
Polynomial, value of 139 377 381
Polynomial, with rational coefficients 341ff
Polynomial, with real coefficients 155
Pontryagin, L.S. 415
Position, false, method of 251
Positive definite forms 174ff
Positive definite quadratic forms 174ff
Positive definiteness of a form 177
Positive index of inertia 172
Postmultiplication 94 99
Power of an element 389
Power sums 322
Power, raising complex numbers to a 120
Power, zero 389
Premultiplication 99
Primary Abelian group 407
Primary components 407
Primary cyclic groups 405 407
Primary group (subgroup) 407
Prime element of a ring 285
Primitive th roots of unity 125
Primitive polynomial 342
Primitive root 391
Principal diagonal 16
Principal minors of a form 175
Principal-axis theorem 219 220
Product direct 406
Product of classes 294 301
Product of matrices 89
Product, scalar (of vectors) 205
Projective geometry 11
Proper rational fraction 156
Proskuryakov, I.V. 414
Pure imaginaries 112
Quadratic equations 225
Quadratic form(s) 306
Quadratic form, canonical 164
Quadratic form, complex 162
Quadratic form, decomposable 172
Quadratic form, definition of 162
Quadratic form, indefinite 177
Quadratic form, matrix of 162
Quadratic form, negative definite 177
Quadratic form, nonsingular 162
Quadratic form, positive definite 174ff
Quadratic form, rank of 162
Quadratic form, real 162
Quadratic form, reduction of to canonical form 161ff
Quadratic form, reduction of to canonical form, theory of 168
Quadratic form, reduction of to principal axes 168 219ff
Quadratic form, semidefinite 177
Quadratic form, theory of 161
Quadratic polynomial 127
Quadric curves and surfaces, theory of 161
Quartic equations 230
Quartic form 306
Quasigroups, theory of 13
Quaternions 111
Quintic equations 232
Quotient 267
Quotient of a polynomial 131
Radius vector 113
Range of values (of a transformation) 197
Rank of a linear transformation 197
Rank of a matrix 69ff
Rank of a matrix, evaluating 72
Rank of a product of matrices 98
Rank of a quadratic form 162
Rank of a system of vectors 68
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