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Proskuryakov I.V. — Problems in Linear Algebra
Proskuryakov I.V. — Problems in Linear Algebra



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Название: Problems in Linear Algebra

Автор: Proskuryakov I.V.

Аннотация:

The topics covered in this problem book include determinants, matrix algebra, polynomial matrices, bilinear and quadratic forms, linear spaces, linear transformations, the Jordan form of matrices, Euclidean space, groups, rings, fields, modules, and tensor algebra.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1985

Количество страниц: 463

Добавлена в каталог: 11.07.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adjoint      153
Adjugate      153
Adjugate determinant      81
Affine spaces      288 289
Affine vector spaces      195
Algebra, tensor      295
Annihilation      86
Annihilator of an element      276
Associated matrix      153
Automorphism      259 268
Basis (pl: bases) conjugate      297
Basis dual      297 298
Basis of a set of vectors      110
Basis orthonormal      206
Basis reciprocal      217
Bessel's inequality      212
Bilinear forms      284
Bilinear functions      284
Binet — Cauchy formula      80
Bivector      305
Block matrices      150
Block triangular matrix      151
Bordering a determinant      73
Canonical forms      183
Cauchy — Bunyakovsky inequality      81 212
Cauchy's theorem      261
Characteristic polynomials      166
Closure, convex      205
Cofactors      65
Commutator      257
Component of a tensor      297
Composition of two quadratic forms      187
Cone, null      286
Congruent modulo n      267
Conjugate basis      297
Contraction of tensors      306
Contravariant components      299
Contravariant discriminant      301
Contravariant law      297
Contravariant metric tensor      300
Contravariant quantities      297
Convex closure      205
Convex set      205
Corner minor      186
Covariant components      299
Covariant discriminant      300
Covariant law      297
Covariant metric tensor      300
Covariant quantities      297
Cyclic space      231
Degenerate form      187
Determinant, Gram      216
Determinant, skew-cyclic      79
Determinant, Vandermonde      36
Diagonal form of a matrix      166
Dimension of a linear manifold      196
Dimension of a linear subspace      227
Direct product      153
Direct sum of two linear subspaces      196
divisors      156
Dual basis      297 298
Dyadic-rational numbers      251
Efimov, N. V.      288 295
Element(s) annihilation of      276
Element(s) free      276
Elementary transformations (or operations) of a matrix      106
Elements of nonzero order      276
Elements of order zero      276
Elements order of      276
Elements periodic      276
Embedding      274
Endomorphism      259
Equality, Parseval      212
Equation(s) $\lambda$-equation      189
Equation(s) parametric      290
Equivalent matrices      147
Essential term      91
Euclidean space      205
Euler identity      79
Euler's function      94
Exponent of nilpotency      148
Extension of a module      279
Factor module      276
Factor, invariant      156
Faddeev, D. K.      6
fibonacci      54
Fibonacci sequence      54
Fields      265
Form(s) (a homogeneous polynomial)      73
Form(s) bilinear      284
Form(s) canonical      183
Form(s) composition of two quadratic      187
Form(s) degenerate      187
Form(s) diagonal (of a matrix)      166
Form(s) Jordan (of a matrix)      166
Form(s) linear      284
Form(s) normal      183
Form(s) orthogonally equivalent quadratic      192
Form(s) quadratic      183 192 284
Function(s) bilinear      284
Function(s) linear      86 284
Function(s) metric      298
Function(s) polylinear      298
Function(s) quadratic      284
Fundamental set (or system) of solutions      121
Gantmakher, F. R.      6 406
Gaussian integers      256 272
Gelfand, I. M.      6
Gram determinant      216
Gram matrix      218
Group(s)      251
Group(s) p-group      261
Group(s) primary      261
Group(s) simple      255 258
Height of a vector      233
Hilbert space      283
Homomorphic mapping      276
Homomorphism, kernel of      275
Hyperplane      289
Ideal      273
Ideal principal      273
Ideal sum of      273
Idempotent matrix      176
Idempotent transformation      235
Image under a transformation      227
Index of inertia      185
Inequality Bessel's      212
Inequality Cauchy — Bunyakovsky      212
Inequality Hadamard      144
Inequality Sylvester's      145
Inequality triangle      213
Inertia, index of      185
Inner product      299
Inner-product space      298
Integer(s) congruent      267
Integer(s) Gaussian      256 272
Invariant factors      156
Involutory matrix      176
Involutory transformation      235
Isomorphic mapping      276
Isomorphism      276
Jordan form of a matrix      166
Jordan Matrix      172
Jordan submatrix      172
Kagan, V. F.      16
Kernel left      287
Kernel of a homomorphism      275
Kernel of a transformation      227
Kronecker delta      141
Kronecker product      90 153
Lagrange — Sylvester interpolation polynomial      179
Lambda ($\lambda$-equation)      189
Laplace theorem      65
Left Kernel      287
Left null space      287
Legendre polynomials      215
Linear dependence of vectors and linear forms      105
Linear forms      284
Linear functions      86 284
Linear manifold      196
Linear of Euclidean and unitary vector spaces      236
Linear of vector spaces      220
Linear spaces      280
Linear subspace      195
Linear transformations      182 220 236 280
Maltsev, A. I.      6
Manifold, linear      196
Mapping homomorphic      276
Mapping isomorphic      276
Matrix (pl: matrices) adjoint      153
Matrix adjugate      153
Matrix and quadratic forms      131
Matrix associated      154
Matrix block      150
Matrix block triangular      151
Matrix computing      134
Matrix diagonal      134
Matrix equivalent      147
Matrix functions of      166
Matrix Gram      218
Matrix Hermitian      1414
Matrix idempotent      143 176
Matrix involutory      143 176
Matrix Jordan      172
Matrix member of a set      196
Matrix nilpotent      148
Matrix normal      147
Matrix nullity of      171
Matrix orthogonal      141
Matrix partitioned      150
Matrix periodic      176
Matrix polynomial      155
Matrix rank of      105 171
Matrix scalar      134 268
Matrix similar      166
Matrix spectrum of      179
Matrix square      134
Matrix sum of two      107
Matrix transition      195
Matrix triangular      145 147
Matrix unimodular      139 159
Matrix unitary      141
Method(s) elimination      118
Method(s) of changing the elements of a determinant      41
Method(s) of isolating linear factors      35
Method(s) of recurrence relations      37
Method(s) of representing a determinant as a sum of determinants      40
Metric function      298
Minimal polynomials      135 166 227
Minor(s)      65
Minor(s) corner      186
Minor(s) principal      144 170
Module(s)      275
Module(s) extension of      279
Module(s) factor      276
Module(s) periodic      278
Module(s) primary      278
Module(s) unital left      276
Multiplication of determinants      74
Nilpotent Jordan submatrix      178
Nilpotent matrices      148
Nonsingular transformation      182
Normal form      183
Normal matrices      147
Normal property of a space      250
Normalized function      87
Null cone      286
Null vector      286
Nullity      171 227
Number(s) Bernoulli      103
Number(s) dyadic-rational      251
Number(s) Euler      102
Order of a tensor      297
Order of an element      276
Orthogonal vectors      206
Orthogonalization of a set of vectors      206
Orthogonally equivalent quadratic forms      192
Orthonormal basis      206
Orthonormal system      141
p-vector      305
Parametric equations      290
Parseval equality      212
Partitioned matrices      150
Periodic element      276
Periodic matrix      176
Periodic module      278
Pfaffian      92
Pfaffian aggregate      92
Pfaffian product      91
Point-vector spaces      288
Polylinear functions      298
Polynomial matrices      155
Polynomial(s) characteristic      166
Polynomial(s) equal      100
Polynomial(s) Lagrange — Sylvester interpolation      179
Polynomial(s) Legendre      215
Polynomial(s) minimal      135 166 227
Pre-image      227
Primary components of a group      263
primary group      261
Primary module      278
Principal ideal      273
Principal minor      144 170
Product direct      153
Product inner      299
Product Kronecker      90 153
Product scalar      299
Product tensor      301 302
Projection of a space      282
Projection of a vector      211
Property, normal (of a space)      250
Pythagoras theorem      213
Quadratic forms      183 192 284
Quadratic functions      284
Radius vector      290
Rank of a matrix      105 171
Rank of a set of vectors      110
Rank of a tensor      297
Reciprocal bases      217
Recurrence relation      37
Residue modulo n      267
Resultant of polynomials      171
Rings      265
Rings of principal ideals      274
Scalar matrix      268
Scalar product      299
Schur's theorem      237
Series, skew      140
Set convex      205
Set member of      196
Shafarevich, I. P.      270
Similar matrices      166
Simple group      255 258
simplex      211
Skew circulant      79
Skew-cyclic determinant      79
Skornyakov, L. A.      295
Sominsky, I. S.      16
Space(s) affine      288
Space(s) affine vector      195
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