Greub W.H. — Linear Algebra :: Электронная библиотека попечительского совета мехмата МГУ

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Greub W.H. — Linear Algebra

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Название: Linear Algebra

Автор: Greub W.H.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3

Год издания: 1967

Количество страниц: 448

Добавлена в каталог: 27.08.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\varphi$ -derivation      148
1-parameter group      237
A $G_{p}$ -gradation      165
Abelian group      2
Adjoint mapping      204
Adjoint matrix      111
Affine coordinate-system      280
Affine coordinates      280
Affine equivalent quadrics      293
Affine mapping      281
Affine space      279
Affine subspace      281
Algebra      139
Algebra of linear transformations      141
Algebra of quaternians      321
Algebraic number      161
Almost finite gradation      166
Alternative theorem      86
angle      183
Anticommutative graded algebra      171
Antiderivation      149
Associative algebra      140
Associativity (groups)      1
Augmented matrix      88
Barybicentric coordinates      208
Basis      11
Basis transformation      91
Bessel's-inequality      189
Bicommutant      403
Bilinear function      63
Binomial formula      171
Boundaries      173
Bounded linear transformation      201
Canonical injection      23
Canonical involution      171
Canonical projection      26
Canonical projection (group)      2
Cauchy-criterion      203
Cayley — Hamilton theorem      399
Center      283
Center of an algebra      150
Chain      4
Chain rule      341
Characteristic coefficients      118
Characteristic equation      116
Characteristic polynomial      118 373
Characteristic polynomial of a matrix      120
Characteristic zero (field)      3
Co-dimension      36
Coboundaries      174
Cocycles      174
Coefficient field      5
Cofactor      111
Cohomology space      174
Column-vectors      82
Commutant      402
Commutative (group)      2
Commutative algebra      140
Compatible gradations      165
Complementary subspace      26
Complete normed linear space      203
Complex vector space      6
components      11
composition      18
Cone with vertex      285
Conjugate determinant-function      313
Conjugate linear transformations      394
Conjugate principal axes      300
Conjugation      312
Connecting mapping      174
continuous curve      232
Continuously differentiable curve      232
Contragradient basis-transformations      92
Convergent sequence      203
Convex subsets      270
Coset (group)      2
Cosine-theorem      184
Covarient components      199
Cramer's solution formula      112
Cross product      194
Cycles      173
Cyclic space      383
Deformable basis      132
Degree of a homogeneous linear mapping      163
Degree of a polynomial      339
Degree of nilpotency      153
DeMoivre's formula      242
Derivation      147
Derived algebra      143
Determinant of a linear transformation      102
Determinant of an $n\times n$ matrix      106
Determinant-function      98
Diagonal mapping      56
Difference space      279
Difference vector      279
Differentiable curve      232
Differential algebra      178
Differential operator      173
Differential space      173
Differentiation map      341
DIMENSION      32
Direct (internal)      24
Direct sum (external)      55
Distance      189
Distributive law (field)      3
Division-algebra      321
Divisor      345
Dual bases      76
Dual determinant-function      109
Dual differential spaces      174
Dual G-graded spaces      174
Dual mappings      67
Dual spaces      64
Eigen-space      211
Eigenvalue      116
Eigenvalues of a matrix      120
Eigenvector      116
Elementary transformation      94
Elements of a matrix      82
ellipse      292
Endomorphism      139
Entries of a matrix      82
Equilateral simplex      283
Equivalent matrices      97
Equivalent vectors      28
Euclid algorithm      344 352
Euclidean space      181 282
Euler — Poincare characteristic      180
Euler — Poincare formula      180
Exact sequence      45
Exact sequence of differential spaces      174
Exchange theorem of Steinitz      16
Expansion-formula      113
Extension field      3
Factor algebra      144
Factor group      3
Factor set      2
Factor space      29
Field      3
Fitting decomposition      378
Fore-cone      270
Function      1
G-graded algebra      169
G-graded differential algebra      178
G-graded factor space      164
G-graded subalgebra      170
G-graded subspace      163
G-graded vector space      162
General linear group      53
General orthogonal group      223

Generalized eigenspaces      375
Generator      383
Graded space      162
Gram determinant      192 314
Greatest common divisor      346
Greatest lower bound      4
Group      1
Group of degrees      162
Group of linear automorphisms      53
Group of permutations      2
Hadamard's inequality      198
Hermitian function      309
Hermitian matrix      310
Homogeneous linear mapping      163
Homogeneous system of linear equations      85
Homogeneous vectors      162
Homology algebra      178
Homology space      173
Homomorphism of algebras      139
Homomorphism of differential algebras      178
Homomorphism of differential spaces      173
Homomorphism of exact sequences      47
Homomorphism of groups      2
Homothetic linear transformation      223
Homotopy operator      179
Hyperbola      292
Hyperplane      281
Ideal      143
Identification      55
Identity element      1
Image space      41
Indefinite bilinear function      249
Index of a bilinear function      252
Index of a pseudo-Euclidean space      264
Induced basis      75
Induced orientation      128
Infinite-dimensional vector space      32
Inhomogeneous system of linear equations      85
Inner product      181
Inner product space      181
Instantaneous axis      239
Integration operator      343
Intersection      23
Intersection number      132
Inverse isomorphism      17
Inverse matrix      90
Involution      18
Irreducible algebra      156
Irreducible polynomial      345
Irreducible space      54 388
Isometric linear mapping      220
Isomorphic      17
Isomorphism of exact sequences      47
Jacobi identity      151
Jordan canonical matrix      391
Kernel      41
Kronecker symbol      75
Lattice      4
Leading coefficient      339
Least common multiple      346
Least upper bound      4
Left ideal      143
Left inverse of a linear mapping      52
Leibniz formula      147
Lie algebra      151
Light-cone      264
Light-cone-vector      264
Linear automorphism      17
Linear closure      23
linear combination      8
Linear function      16
Linear isomorphism      17
Linear mapping      16
Linear transformation      17
Linearly dependent vectors      9
Linearly independent vectors      10
Linearly ordered elements      4
Lorenz transformation      275
Lower bound      4
Lower triangular matrix      90
Mapping      1
Matrix      82
Metric normal-form      30
Metrically equivalent quadrics      302
Minimum polynomial      357
Minkowsky-space      275
Minor      113
Monic polynomial      339
Monomial polynomial      339
Multiple      345
Multiplication operator      140
N-dimensional affine space      279
n-space over      7
Neighbourhood      38
Nilpotent element      153
Nilpotent linear transformation      121 406
Nilpotent part      365
Non-degenerate bilinear function      63
Non-trivial linear relation      9
Norm of a vector      181 310
Norm-function      200
Norm-topology      201
Normal form of a matrix      94
Normal form of a quadric      290
Normal linear transformation      207 316
Normal-vector      299
Normed determinant-function      191
Normed linear space      200
Nullspaces      63
Opposite algebra      140
Orientation      127
Orientation preserving      127
Oriented angle      191
Origin      280
Orthocroneous transformation      275
Orthogonal basis      186
Orthogonal complement      66 188
Orthogonal matrix      188
Orthogonal projection      189 214
Orthogonal vectors      66 182
p-th Betti number      177
p-th dimensional parallelepiped      192
p-th homology space      176
parabola      292
Parallel affine subspaces      281
Parallelogram-identity      245
Partially ordered set      4
Past-cone      270
Pauli-matrices      332
Poincare series      166
Point      279
Polar subspace      292
Polynomial      340
Polynomial function      350
Positive basis      127
Positive definite      248
Positive definite Hermitian function      309
Positive gradation      162
Positive selfadjoint transformation      213
Positive semidefinite symmetric bilinear function      248
Positive vector      280
Prime polynomial      345
Principal axes      300
Principal minors      114
Product (algebra)      139
Product of matrices      89
Projection operator      59
Proper rigid motion      284
Proper rotation      224
Pseudo-Euclidean rotation      272

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