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| Авторизация |
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| Hefferon J. — Linear algebra |
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| Предметный указатель |
Matrix 13
Matrix equivalence 242—249
Matrix equivalence, canonical form 245
Matrix equivalence, definition 244
Matrix, adjoint 328
Matrix, antisymmetric 139
Matrix, augmented 14
Matrix, block 245 311
Matrix, change of basis 238
Matrix, characteristic polynomial 362
Matrix, cofactor 327
Matrix, column 13
Matrix, column space 126
Matrix, conditioning number 71
Matrix, determinant 294 299
Matrix, diagonal 210 225
Matrix, diagonalizable 356
Matrix, diagonalized 244
Matrix, elementary reduction 227 275
Matrix, entry 13
Matrix, equivalent 244
Matrix, identity 221 225
Matrix, incidence 229
Matrix, inverse 329
Matrix, main diagonal 225
Matrix, Markov 230 285
Matrix, matrix-vector product 198
Matrix, minimal polynomial 221 382
Matrix, minor 327
Matrix, multiplication 216
Matrix, nilpotent 372
Matrix, nonsingular 27 208
Matrix, orthogonal 289
Matrix, orthonormal 287—292
Matrix, permutation 226
Matrix, rank 207
Matrix, representation 197
Matrix, row 13
Matrix, row equivalence 50
Matrix, row rank 124
Matrix, row space 124
Matrix, scalar multiple 213
Matrix, similar 324
Matrix, similarity 353
Matrix, singular 27
Matrix, skew-symmetric 311
Matrix, submatrix 303
Matrix, sum 213
Matrix, symmetric 118 139 214 221 229 268
Matrix, trace 214 230 400
Matrix, transition 281
Matrix, transpose 19 126 214
Matrix, triangular 204 230 330
Matrix, unit 223
Matrix, Vandermonde 311
Matrix:form 56
Mean, arithmetic 44
Mean, geometric 44
Member A-7
Method of powers 401—404
Minimal polynomial 221 382
Minor 327
Morphism 161
Multilinear 304
Multiplication, matrix-matrix 216
Multiplication, matrix-vector 198
MUPAD 62
Mutual inclusion A-7
Natural representative A-12
networks 72—77
Networks, Kirchhoff's Laws 73
Nilpotent 370—380
Nilpotent, canonical form for 376
Nilpotent, definition 372
Nilpotent, matrix 372
Nilpotent, transformation 372
Nilpotentcy, index 372
Nonsingular 208 232
Nonsingular, homomorphism 190
Nonsingular, matrix 27
Normalize 258
Nullity 188
NullSpace 188
Nullspace, closure of 369
Nullspace, generalized 369
Octave 62
Odd functions 99 137
One-to-one function A-9
Onto function A-9
Opposite map 290
Order of a recurrence 408
Ordered pair A-8
Orientation 321 324
Orthogonal 42
Orthogonal basis 256
Orthogonal complement 263
Orthogonal matrix 289
Orthogonal mutually 255
Orthogonal projection 263
Orthogonalization 257
Orthonormal basis 258
Orthonormal matrix 287—292
Pair, ordered A-8
Parallelepiped 321
Parallelogram rule 34
PARAMETER 13
Partial pivoting 70
Partition A-10—A-12
Partition, matrix equivalence classes 244 246
Partition, row equivalence classes 51
Partitions into isomorphism classes 170
Permutation 307
Permutation expansion 308 312 334
Permutation, inversions 313
Permutation, matrix 226
Permutation, signum 314
Perp 263
Perpendicular 42
Perspective triangles 343
Physics problem 1
Pivoting on rows 4
Pivoting, full 70
Pivoting, partial, scaled 70
Plane figure 287
Plane figure, congruence 287
Point at infinity 343
Point in projective plane 340
Polynomial of map, matrix 381
Polynomial, even 400
Polynomial, minimal 382
Polynomials, division theorem 350
Populations, stable 405—406
Potential 72
Powers, method of 401—404
Preserves structure 176
Probability vector 281
Projection 176 185 250 268 387
Projection along a subspace 260
Projection into a line 251
Projection into a subspace 260
Projection, central 337
Projection, central, vanishing point 337
Projection, orthogonal 251 263
Projective geometry 337—347
Projective geometry Duality Principle 342
Projective plane, ideal line 343
Projective plane, ideal point 343
Projective plane, lines 341
Proof techniques, induction 23
Proper subspace 92
| Proper, subset A-7
Proposition A-1
Propositions, equivalent A-3
Quantifier A-3
Quantifier, existential A-4
Quantifier, universal A-4
Quantifiers A-3
RANGE A-8
Rangespace 184
Rangespace, closure of 369
Rangespace, generalized 369
Rank 128 207
Rank of a homomorphism 184 189
Rank, column 126
Recurrence 327 408
Recurrence, homogeneous 408
Recurrence, initial conditions 408
Reduced echelon form 47
Reflection 290
Reflection (or flip) about a line 163
Reflection, glide 290
Reflexivity A-10
Relation A-10
Relation, equivalence A-10
Relation, reflexive A-10
Relation, symmetric A-10
Relation, transitive A-10
Relationship, linear 103
Representation of a matrix 197
Representation of a vector 116
Representative A-12
Representative for row equivalence classes 58
Representative of matrix equivalence classes 245
Representative of similarity classes 395
Representative, canonical A-12
Rescaling rows 4
Resistance 72
Resistance:equivalent 76
resistor 72
Restriction A-10
Rigid motion 287
Rotation 274 290
Rotation (or turning) 163
Rotation (or turning), represented 200
Row 13
Row equivalence 50
Row rank, full 131
Row space 124
Row, rank 124
Row, vector 15
scalar 80
Scalar multiple, matrix 213
Scalar multiple, vector 15 34 80
Scalar product 40
Scaled partial pivoting 70
Schwartz inequality 41
SciLab 62
Self composition of maps 367
Sense 321
SEQUENCE A-8
Sequence, concatenation 134
Set A-7
Set, complement A-7
Set, element A-7
Set, empty A-8
Set, intersection A-8
Set, member A-7
Set, union A-8
Sets A-7
Sets, dependent, independent 103
Sets, empty 105
Sets, mutual inclusion A-7
Sets, proper subset A-7
Sets, span of 95
Sets, subset A-7
sgn, seesignum 314
Signum 314
Similar 298 324
Similar matrices 353
Similar triangles 290
Similar, canonical form 394
Similarity 353—366
Similarity transformation 366
Single precision 68
Singular matrix 27
SIZE 319 321
Skew 277
Skew-symmetric 311
span 95
Span of a singleton 99
Spin 149
Square root 400
Stable populations 405—406
Standard basis 114
State 281
State, absorbtive 281
Statics problem 5
String 373
String of basis vectors 371
String, basis 373
Structure, preservation 176
SubMatrix 303
subspace 91—101
Subspace, closed 93
Subspace, complementary 136
Subspace, definition 91
Subspace, direct sum 135
Subspace, improper 92
Subspace, independence 135
Subspace, invariant 391
Subspace, orthocomplement 139
Subspace, proper 92
Subspace, sum 132
Sum of matrices 213
Sum of subspaces 132
Sum, vector 15 34 80
Summation notation for permutation expansion 308
Swapping rows 4
Symmetric matrix 118 139 214 221
Symmetry A-10
System of linear equations 2
System of linear equations, Gauss' method 2
System of linear equations, solving 2
Theorem A-1
Trace 214 230 400
Transformation, characteristic polynomial 362
Transformation, composed with itself 367
Transformation, diagonalizable 356
Transformation, eigenspace 362
Transformation, eigenvalue, eigenvector 359
Transformation, Jordan form for 394
Transformation, minimal polynomial 382
Transformation, nilpotent 372
Transformation, nilpotent, canonical representative 376
Transformation, projection 387
Transformation, size change 321
Transition matrix 281
Transitivity A-10
Translation 287
TRANSPOSE 19 126
Transpose, determinant 309 317
Transpose, interaction with sum and scalar multiplication 214
Triangle inequality 40
Triangles, similar 290
Triangular matrix 230
Triangularization 204
Trivial space 84 114
Turning map 163
union A-8
Unit matrix 223
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