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Hefferon J. — Linear algebra
Hefferon J. — Linear algebra

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Название: Linear algebra

Автор: Hefferon J.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Количество страниц: 449

Добавлена в каталог: 22.10.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Accuracy of Gauss' method      68—71
Accuracy, rounding error      69
Addition, vector      80
Additive inverse      80
Adjoint matrix      328
angle      42
Antipodal      340
Antisymmetric matrix      139
Argument      A-8
Arrow diagram      217 233 238 242 353
Augmented matrix      14
Automorphism      163
Automorphism, dilation      163
Automorphism, reflection      163
Automorphism, rotation      163
Back-substitution      5
Base step of induction      A-5
Basis      113—124
Basis, change of      238
Basis, definition      113
Basis, orthogonal      256
Basis, orthogonalization      257
Basis, orthonormal      258
Basis, standard      114 352
Basis, standard over the complex numbers      352
Basis, string      373
Best fit line      269
Block matrix      311
box      321
Box, orientation      321
Box, sense      321
Box, volume      321
C language      68
Canonical form for matrix equivalence      245
Canonical form for nilpotent matrices      376
Canonical form for row equivalence      58
Canonical form for similarity      394
Canonical representative      A-12
Cauchy — Schwartz inequality      41
Cayley — Hamilton theorem      384
Central projection      337
Change of basis      238—249
Characteristic equation      362
Characteristic polynomial      362
Characteristic vectors, values      359
Characterized      172
Characterizes      246
Chemistry problem      1 9 22
Circuits, parallel      73
Circuits, series      73
Circuits, series-parallel      74
Class, equivalence      A-12
Closure      95
Closure of nullspace      369
Closure of rangespace      369
Codomain      A-8
Cofactor      327
column      13
Column rank, full      131
Column space      126
Column, rank      126
Column, vector      15
Complement      A-7
Complementary subspaces      136
Complementary subspaces, orthogonal      263
Complex numbers, vector space over      90
Component      15
composition      A-9
Composition, self      367
Computer algebra systems      62—63
Concatenation      134
Conditioning number      71
Congruent figures      287
Congruent plane figures      287
Contradiction      A-6
Contrapositive      A-3
Convex set      183
Coordinates with respect to a basis      116
Coordinates, homogeneous      340
Corollary      A-1
Correspondence      161 A-9
Coset      193
Cramer's rule      331—333
Cross product      298
Crystals      143—146
Crystals, diamond      144
Crystals, graphite      144
Crystals, salt      143
Crystals, unit cell      144
da Vinci, Leonardo      337
Determinant      294 299—318
Determinant, cofactor      327
Determinant, Cramer's rule      332
Determinant, definition      299
Determinant, exists      309 315
Determinant, Laplace expansion      327
Determinant, minor      327
Determinant, permutation expansion      308 312 334
Diagonal matrix      210 225
Diagonalizable      356—359
Difference equation      408
Difference equation, homogeneous      408
Dilation      163 276
Dilation, representing      203
DIMENSION      121
Dimension, physical      152
Direct map      290
Direct sum      131
Direct sum of two subspaces      136
Direct sum, )      140
Direct sum, definition      135
Direct sum, external      168
Direct sum, internal      168
Direction vector      35
Distance-preserving      287
Division theorem      350
Domain      A-8
Dot product      40
DOUBLE PRECISION      69
Dual space      194
Echelon form      5
Echelon form, free variable      12
Echelon form, leading variable      5
Echelon form, reduced      47
Eigenspace      362
Eigenvalue, eigenvector of a matrix      360
Eigenvalue, eigenvector of a transformation      359
Element      A-7
Elementary matrix      227 275
Elementary reduction operations      4
Elementary reduction operations, pivoting      4
Elementary reduction operations, rescaling      4
Elementary reduction operations, swapping      4
Elementary row operations      4
Empty set      A-8
Entry      13
Equivalence relation      A-10 A-11
Equivalence relation, isomorphism      169
Equivalence relation, matrix equivalence      244
Equivalence relation, matrix similarity      353
Equivalence relation, row equivalence      50
Equivalence, class      A-12
Equivalence, class, canonical representative      A-12
Equivalence, relation      A-10
Equivalence, representative      A-12
Equivalent statements      A-3
Erlanger Program      287
Euclid      287
Even functions      99 137
Even polynomials      400
External direct sum      168
Fibonacci sequence      407
Field      141—142
Field, definition      141
Finite-dimensional vector space      119
Flat      36
FORM      56
Free variable      12
Full column rank      131
Full row rank      131
Function      A-8
Function, argument      A-8
Function, codomain      A-8
Function, composition      216 A-9
Function, correspondence      A-9
Function, domain      A-8
Function, even      99
Function, identity      A-9
Function, inverse      232 A-9
Function, inverse image      185
Function, left inverse      231
Function, multilinear      304
Function, odd      99
Function, one-to-one      A-9
Function, onto      A-9
Function, range      A-8
Function, restriction      A-10
Function, right inverse      231
Function, structure preserving      161 165
Function, structure preserving, seehomomorphism      176
Function, two-sided inverse      232
Function, value      A-8
Function, well-defined      A-8
Function, zero      177
Fundamental theorem of linear algebra      268
Gauss — Jordan      47
Gauss' method      2
Gauss' method, accuracy      68—71
Gauss' method, back-substitution      5
Gauss' method, elementary operations      4
Gauss' method, Gauss — Jordan      47
Generalized nullspace      369
Generalized rangespace      369
Geometry of Linear Maps      274—280
Gram — Schmidt process      255—260
Historyless, Markov chain      281
Homogeneous coordinate vector      340
Homogeneous coordinates      292
Homogeneous equation      21
Homomorphism      176
Homomorphism, composition      216
Homomorphism, matrix representing      195—205
Homomorphism, nonsingular      190 208
Homomorphism, nullity      188
Homomorphism, nullspace      188
Homomorphism, rangespace      184
Homomorphism, rank      207
Homomorphism, zero      177
Ideal line      343
Ideal point      343
Identity, function      A-9
Identity, matrix      225
If-then statement      A-2
Ill-conditioned      69
Image, under a function      A-9
Improper subspace      92
Incidence matrix      229
Index of nilpotency      372
Induction      23 A-5
Inductive step of induction      A-5
Inherited operations      82
Inner product      40
Input-output analysis      64—67
Internal direct sum      135 168
Intersection      A-8
Invariant subspace      379
Invariant subspace, definition      391
Inverse      232 A-9
Inverse function      232
Inverse image      185
Inverse, additive      80
Inverse, exists      232
Inverse, left      232 A-9
Inverse, matrix      329
Inverse, right      232 A-9
Inverse, two-sided      A-9
inversion      313
Isometry      287
Isomorphism      159—175
Isomorphism of a space with itself      163
Isomorphism, characterized by dimension      172
Isomorphism, definition      161
Jordan block      390
Jordan form      381—400
Jordan form, represents similarity classes      394
Kernel      188
Kirchhoff's laws      73
Klein, F.      287
Laplace expansion      326—330
Laplace expansion, computes determinant      327
Leading variable      5
Least squares      269—273
Lemma      A-1
Length      39
Leontief, W.      64
Line at infinity      343
Line in projective plane      341
Line of best fit      269—273
Line, best fit      269
linear combination      52
Linear Combination Lemma      53
Linear equation      2
Linear equation, coefficients      2
Linear equation, constant      2
Linear equation, homogeneous      21
Linear equation, inconsistent systems      269
Linear equation, satisfied by a vector      15
Linear equation, solution of      2
Linear equation, solution of, Gauss – Jordan      47
Linear equation, solution of, Gauss' method      3
Linear equation, solutions of, Cramer's rule      332
Linear equation, system of      2
Linear map, dilation      276
Linear map, reflection      290
Linear map, rotation      274 290
Linear map, seehomomorphism      176
Linear map, skew      277
Linear map, trace      400
Linear recurrence      408
Linear recurrences      407—414
Linear relationship      103
Linear surface      36
Linear transformation, seetransformation      179
Linear transpose operation      130
Linearly dependent      103
Linearly independent      103
LINPACK      62
MAP      A-8
Map, distance-preserving      287
Map, extended linearly      173
Map, self composition      367
Maple      62
Markov chain      281
Markov chain, historyless      281
Markov chains      281—286
Markov matrix      285
Material implication      A-2
Mathematica      62
Mathematical induction      23 A-5
MATLAB      62
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