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Lang S. — Linear Algebra

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Название: Linear Algebra

Автор: Lang S.

Аннотация:

The present book is meant as a text for a course in linear algebra, at the undergraduate level. Enough material has been included for a one-year course, but by suitable omissions, it will also be easy to use the book for one term.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 1972

Количество страниц: 400

Добавлена в каталог: 12.05.2013

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

Предметный указатель

Abelian      327
Absolute value      36
Abstract field      352
Adjoint      228
Algebra      350
Algebraically closed      352 374
Alternating product      195 311
Angle between planes      28
Angle between vectors      22
Antilinear      160
Area      202
Automorphism      329 333
Basis (of abelian group)      344
Basis (of vector space)      47
Beginning point      8
Bessel inequality      137
Bilinear form      215
Bilinear map      152
Bounded from below      369
Canonical homomorphism      362
Characteristic polynomial      252 255
Characteristic value      247
Coefficient of a polynomial      242
column      60
Column rank      148
Column vector      59 62
Commutative      327
complex numbers      34
Component      134
Component of matrix      59
Composite mapping      86
Congruent      355
conjugate      34 377
Constant term      242
Convex closure      371
Convex set      113 365
Convolution      350
Coordinate functions      85
Coordinates of vector      4 48
Coordinates with respect to a basis      48
Coset      336
Cramer's rule      182
Curve      85
Cyclic      297 298
Cyclic group      341
Degree of polynomial      242
Derivation      353
Determinant      167
Diagonal elements      63
Diagonal matrix      62
Diagonalize      128 218
Differential equations (linear)      294
DIMENSION      52
Dirac functional      161
Direct product      57 329
Direct sum      55
Direction      9 16
Distance      16
Divide      285
Dot product      10
Dual basis      161
Dual space      159
Eigenspace      247 292
Eigenvalue      247
Eigenvector      246
Elimination      80
End point      8
Endomorphism      358
Equivalence relation      375
Equivalent vectors      8
Euclidean algorithm      281
Even permutation      190
Expansion of determinants      170 174
Exponent of element      341
Extreme point      369
Factor group      339
Factor module      362
Faithful      336
Fan      257
Fan basis      257
Field      39
Finite dimensional      53
Finite group      329
FORM      215
Fourier coefficient      134 143
Functional      159
g.c.d.      285
General linear group      328
Generate      43
Generators of a group      330
Generators of a vector space      43
Generators of ideal      284 351
Gradient      164
Gram — Schmidt orthogonalization      138
Greatest common divisor      285
Group      327
Half space      366
Hamilton — Cayley      260
Hermitian form      227
Hermitian map      228
Hermitian matrix      228
Hermitian product      142
Homogeneous equations      64
Homomorphism      330
Hyperplane      27
Ideal      283
Identity mapping      88
Image      83 99
Index of a subgroup      337
Index of nullity      237
Index of positivity      238
Induction      373
Infinite dimensional      53
Injective      87
Inner automorphism      334
Intersection      39 44
Invariant subspace      257 273 295
Inverse      73 88
Inverse image      253
Invertible      73 329
Irreducible      286
Isomorphism of groups      332
Isomorphism of vector spaces      106
Jordan Basis      298
Jordan normal form      299
Kernel      98 354
Kernel of ring homomorphism      268
Krein — Milman theorem      285
Leading coefficient      242
Left ideal      351
Length      13 133

Line      24
Line segment      109
linear combination      43
Linear mapping      91 93 358
Linear polynomial      243
Linearly dependent      46
Linearly independent      46
Located vector      9
Mapping      83
Matrix      59 120
Maximal set of linearly independent elements      49
Minimal polynomial      289
Module      357
Modulo an ideal      355 362
Monic      288
Multilinear map      315
Multiplication of matrices      69
Multiplicity      243 288
Multiplicity of eigenvalue      255
Negative definite      273
Nilpotent      79 259
Non-degenerate      69 131
Non-singular      73
Norm of a vector      13 133
normal      274 338
Null form      157
Null space      157
Odd permutation      190
Operator      105 222
Opposite direction      16
Order      329
Orientation      382
Orthogonal      12 132 141 161
Orthogonal basis      137
Orthogonal map      231
Orthonormal      138
parallel      9 28
Parallelogram      97
Period      342
Permutation      186
Perpendicular      12 132 161
Plane      26
Point      4
Polarization      229
Polynomial      241
Positive      226 274
Positive definite operator      226 272
Positive definite product      133 142
Prime number      291
Principal left ideal      351
Projection      19 134
Proper subset      39
Pythagoras theorem      18
Quadratic form      220 224
Rank      149 200
Rational function      377
Relatively prime      285
Represent      163 216 224 229
Representation      336
Representative      355
Residue classes mod an ideal      355
Right ideal      351
Right multiplication      359
Rigid motion      334
Ring      349
Ring homomorphism      354
Root      243
Root of unity      343
Rotation      233
Row      59 62
Row rank      148
Same direction      16
scalar      40
Scalar product      10 131
Schur's lemma      295
Schwarz inequality      135
Self-adjoint      228
Separating hyperplane      367
Set      39
Sign of permutation      189
Similar matrices      128
Simple subspace      295 361
Simultaneously diagonalizable      271
Skew symmetric matrix      102 220
Spanned      115
Special linear group      328
Spectral basis      271
Spectral theorem      268
Square matrix      60
Strictly upper triangular      78
Subfield      40
Subgroup      330
Submodule      361
Subring      352
Subset      39
subspace      42
Sum of subspaces      45 55
Supporting hyperplane      368
Surjective      87
Sylvester's theorem      235
Symmetric form      216
Symmetric group      328
Symmetric linear map      224
Symmetric matrix      62
Tensor product      308
Trace      77
Translation      89
Transpose of linear map      224
Transpose of matrix      62
Transposition      186
triangle      112
Triangle inequality      23
Triangulable      258
Trivial group      329
Trivial solution      42
Two-sided ideal      351
union      39
Unit element      330 350
Unit ideal      284
Unit vector      15 133
Unitary map      231 275
Unitary matrix      233
Upper triangular      78
Value      83
Vandermonde determinant      179
Vector      9 41 42
Vector space      40
Volume      202
Wedderburn — Rieffel theorem      360
Zero map      93
Zero matrix      60

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