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Авторизация |
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Поиск по указателям |
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Nicholson W.K. — Linear Algebra with Applications |
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Предметный указатель |
Matrix, upper triangular 78
Matrix, values 251
Matrix, Vandermonde 116 134
Matrix, vectors 251
Matrix, zero matrix 36
Median of a tetrahedron, I 55
Median of a triangle 155
midpoint 150
Minor of a matrix 109
Mirkil, H 102
Mlpoient matrix 260
Modulus of a complex number 467
Moore — Penrose inv erse 331
Multiplication of matrices 43
Multiplication of matrices, properties of 47
Multiplication rule lor complex numbers 471
Multiplicity of eigenvalues 265 394
Multiplicity ol a root 265 394
n-tuple 187
Negative of a function 191
Negative of a geometric vector 142
Negative of a matnx 36 190
Negative of an H-inplc 188
Negative uniqueness of 194 197
Network flow 27
Network, electrical 29
Norm 303 425
Normal equations 180 325
Normal matrix 310
Normal vector for a plane 166
Normalizing 272 432
Null space of a linear transformation 353
Null space of a matrix 200
Null space of function 462
Null space of objective function 482 486 489
Null space of odd polynomial 219
Nullity oflincar transformation 354
One-to-one linear transformation 355
Onto linear transformations 355
Open scctor of an economy 93
Operator (see Linear operator)
Ordered basis 371
Ordered n-tuple 187
Ordered n-tuple, dot-product 44 270
Ordered n-tuple, sum and difference 188
Ordered pair 187
Ordered triple 187
Origin 147
Orthogonal 277 436
Orthogonal, basis 273 433
Orthogonal, complement of a subspacc 277 436
Orthogonal, diagonalization 283 441
Orthogonal, lemma 274 434
Orthogonal, Matrix 281 450
Orthogonal, projection 278 437
Orthogonal, set of vectors 271 307 431
Orthogonal, vectors 157 160 307
Orthogonalizmion algorithm 275
Orthonormal set of vectors 271 307 431
Parallel vectors 142
Parallelepiped 174
Parallelogram, area of 173
Parallelogram, rule 143 469
PARAMETER 3 151
Parametric, equations ol a line 151
Parametric, lorm of solutions 2
Parseval’s formula 441
Partition, of a matrix 52
Permutation matrix 85 288 387
Pivot 492
Plane, complex 468
Plane, normal to 166
Plane, scalar equation 166
Plane, vector equation 167
PLU-factorization 86
Polar norm of a complex number 470
Polynomial 191
Polynomial, associated to a linear recurrence 414
Polynomial, characteristic 253 306
Polynomial, coefficients 191
Polynomial, degree 191
Polynomial, equality 192
Polynomial, evaluation at a matrix 260
Polynomial, evaluation at the shill operator 417
Polynomial, evaluation of 201 260
Polynomial, even 219
Polynomial, factor theorem 239
Polynomial, fundamental theorem of algebra 477
Polynomial, interpolating, I 32
Polynomial, Lagrange interpolation expansion for 242
Polynomial, Lagrange polynomials 242
Polynomial, Legendre polynomials 436
Polynomial, odd 219
Polynomial, remainder theorem 239
Polynomial, root 201
Polynomial, Taylor's theorem lor 24
Polynomial, vector space ot 192
Polynomial, zero polynomial 191 192
Position vector of a point 147
Positive definite, matrix 289 293 424
Positive definite, quadratic form 321
Positive vector ol a point 147
Power method 298
Pre-image of a subspace 351
principal argument 470
Principal argument, submatrix 291
Principal Axes Theorem 283 445
Principle of Mathematical Induction 502
Probabilities 96
Product of matrices 44
Product theorem for determinants 120
Projection 162 278 4
Projection, linear operator 448
Projection, matrix 281 288
Projection, orthogonal 277 437
Projection, theorem 278 437
Pythagorean Theorem 156 165 272 432
Quadratic equation 323
Quadratic form 313 425
Quadratic form, completely dtagonali/ed 321
Quadratic form, diagonalization of 3 3
Quadratic form, index of 321
Quadratic form, positive definite 323
Quadratic form, principal axes for 115
Quadratic form, rank of 321
Quadratic form, Sylvester's law 320
Quadratic, discriminant of 475
Quadratic, formula 475
Quadratic, irreducible 475
Quadratic, real 475
Radian measure 469
Range of a linear transformation 353
Range of a matrix 200
Rank of a linear transformation 354
Rank of a matrix 21 230
Rank of a quadratic form 321
Rayleigh quotients 298
Real axis 468
Real eigenvalues 256 444
Real part of complex numbers 465
Recurrence relation, associated polynomial 414
Recurrence relation, length 412
Recurrence relation, linear 267 411
Recurrence relation, space of solutions 411
Reduced 11
Reducible linear operator 397
Reflection 343 349 452 458
Relation to invertibility 231
Relation to null space 21 234
Relation to null space, theorem 229
| Remainder theorem 239
Restriction of a linear operator 389
Rhombus 161
Right-hand coordinates 175
Right-hand rule 175
Root of a polynomial 201
Root of a quadratic 475
Root of unity 473 474
Root, complcx 475
Root, multiplicity of 265 394
Rotations 343 349 458
Row matnx 34
Row of a matrix 34
Row operations 8 68
Row operations for determinants 113
Row space 228
Row-cchelon matnx 11
Row-echelon form 11
Row-equivalent matrices 77
scalar 38 189
Scalar equation of a plane 166
Scalar linear transformations 343
Scalar matnx 105
Scalar multiplication 38 144 189
Scalar multiplication of functions 192
Scalar multiplication of geometne vectors 144
Scalar multiplication of linear transformations 406
Scalar multiplication of matrices 38
Scalar multiplication of n-tuples 188
Scalar multiplication of polynomials 192
Scalar product 157
Schmidt. E 275
schur 1 308
Schur’s Theorem 309
Schwarz inequality 427
Schwarz, H A 427
Seneta, B 92
Sequences 411
Sequences, constant 411
Sequences, equality 411
Sequences, Lucas 419
Sequences, power 411
Sequences, satisfying a linear recurrence 411
Sequences, vector spaccof 411
Shear 342
Shift operator 417
Signature of a quadratic form 383
Similar, matrices 256 383
Similar, orthogonally 362
Similarity invariant 257 383
simple harmonic motion 248
Simplex algorithm 4
Simplex algorithm, basic columns 491 495
Simplex algorithm, basic feasible solutions 491 495
Simplex algorithm, basic variables 491 495
Simplex algorithm, degeneration 499
Simplex algorithm, departing variable 493
Simplex algorithm, entenng variable 492
Simplex algorithm, flow chart 496
Simplex algorithm, objective function 482 486 489
Simplex algorithm, pivot columtt 492
Simplex algorithm, pivot entry 492
Simplex algorithm, prototype example 490
Simplex algorithm, unbounded 494
Sine of an angle 469
Size of a matnx 34 38
Skew — Hermitian matrix 312
Skew-symmetnc matrix 43
Skew-symmetnc matrix, operator 448
Slack variables 490
Slack variables, tableau 495
Snell, J. L 102 481
Solutions to a system of equations 2
Solutions to a system of equations, general 3
Solutions to a system of equations, linear combinations 55
Span of a set of vectors 204
Spanning set 204
Spanning set for 204
Spectral theorem 310
Spectral theorem, real 284
Spectrum 284
Spring constant 249
Square matrix 34
Standard, basis 214 303
Standard, inner product in C 303
Standard, matrix of a linear transformation 349
Standard, position for an angle 469
Stewart, G. W 301
Stochastic matrix 91 99
Stochastic matrix, basis of 223
Stochastic matrix, complement of 395
Stochastic matrix, complex 311
Stochastic matrix, dimension of 223
Stochastic matrix, direct sum of 395
Stochastic matrix, doubly 105
Stochastic matrix, intersection of 219 394
Stochastic matrix, invariant 388
Stochastic matrix, orthogonal complement of 277 436
Stochastic matrix, pre-image of 351
Stochastic matrix, projection on 278
Stochastic matrix, regular 102
Stochastic matrix, subspace 198
Sum of 226 394
Sum of functions 192
Sum of geometric vectors 143
Sum of linear transformations 379
Sum of matrices 35
Sum of ordered n-tuples 188
Sum of solutions to equations 50
Sum of subspaces 226 394
Sum of test 198
Sum of zero subspace 199
Sum, pointwise 192
Sylvester’s law of inertia 320
Symmetric, bilinear form 324
Symmetric, matrix 42 283
Symmetric, operator 444
System of linear equations 1
Taylor’s Theorem 240
Terminal point 141
tetrahedron 155
Thompson, G. L 102 481
Tnangulation algorithm 404
Transformations, tee linear transformations trace of a matrix 56 257
Transformations, tee linear transformations trace of an operator 386
Transition matrix for Markov chain 98
Transition probabilities 96 98
Translation 460
TRANSPOSE 41
Triangle, altitude of 161
Triangle, centroid of 155
Triangle, inequality 165 428 468
Triangle, median of 155
Triangular matrix 90
Triangular matrix, angle between 156
Triangular matrix, block 118
Triangular matrix, components 147
Triangular matrix, cross product 168
Triangular matrix, direction vector ol a line 150
Triangular matrix, distance formula 156
Triangular matrix, dot product 157
Triangular matrix, equality 141
Triangular matrix, equation of a line 151
Triangular matrix, equation of a plane 167
Triangular matrix, initial point 141
Triangular matrix, Jacobi identity 177
Triangular matrix, Lagrange identity 172
Triangular matrix, length 141
Triangular matrix, lower 78
Triangular matrix, magnitude 141
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