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| Hefferon J. — Linear algebra |
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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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