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Авторизация |
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Поиск по указателям |
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Lin I.H. — Geometric Linear Algebra. Vol. 1 |
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Предметный указатель |
Adjoint linear operator 422 754 781
Adjoint linear operator (also called) dual operator in dual space 422 754
Adjoint linear operator, self-adjoint or symmetric operator 782 786
Adjoint matrix 336 731
Affine basis (or frame) 9 10 19 31 34 71 239 324 326 362 580 640
Affine basis, base point (origin) 9 10 19 31 34 71 239 324 326 362 580 640
Affine basis, coordinate vector 10 34 326 640
Affine basis, orthonormal affine basis 613 625
Affine coordinate system 19 34 38 324 326 328 362 640
Affine coordinate system, affine coordinate 19 72 239 363 641
Affine coordinate system, barycenter 19 72 363
Affine coordinate system, barycentric coordinate 19 72 363 642
Affine dependence of points 32 71 239 325 362 580 640
Affine geometry 292 640
Affine geometry invariant 19 90 286 374 636 638 679
Affine group 238 240 580 581 656
Affine independence of points 33 71 239 325 362 580 640
Affine invariant 19 90 286 310 374 636
Affine space 9 12 31 34 235 324 326 640
Affine space, n-dimensional 235
Affine space, n-dimensional affine motion 237 240
Affine space, n-dimensional affine subspace 236
Affine space, n-dimensional affine transformation or mapping 237
Affine space, n-dimensional base point 235
Affine space, n-dimensional difference space 235
Affine space, n-dimensional difference vector 236
Affine space, n-dimensional free vector 235
Affine space, n-dimensional position vector (with initial point and terminal point) 235
Affine space, n-dimensional zero vector 235 236
Affine space, one-dimensional 8 12
Affine space, three-dimensional 324 326
Affine space, two-dimensional 31 36
Affine subspace 67 236 359 425 640 724
Affine subspace, coincident 645
Affine subspace, dimension 235
Affine subspace, dimension (or intersection) theorem 644
Affine subspace, hyperplane 641
Affine subspace, k-dimensional plane 640
Affine subspace, operation of affine intersection 644
Affine subspace, operation of affine subspaces 643
Affine subspace, operation of affine sum 644
Affine subspace, parallel 645
Affine subspace, relative positions of affine subspaces 645
Affine subspace, skew 645
Affine transformation or mapping or motion 16 18 47 67 73 83 237 250 326 338 364 366 580 581 655
Affine transformation or mapping or motion, (three-way) stretch 611
Affine transformation or mapping or motion, (three-way) stretch, enlargement 611 656
Affine transformation or mapping or motion, (three-way) stretch, orthogonal stretch 611
Affine transformation or mapping or motion, (three-way) stretch, similarity 611 656
Affine transformation or mapping or motion, decomposition of affine transformation 241 580
Affine transformation or mapping or motion, invariant affine subspace 251 591
Affine transformation or mapping or motion, invariant point 251 591
Affine transformation or mapping or motion, invariant point, subspace of invariant points 251 591
Affine transformation or mapping or motion, matrix representation 239 580 581
Affine transformation or mapping or motion, one-way stretch, stretching 255 596 597
Affine transformation or mapping or motion, one-way stretch, stretching, orthogonal one-way stretch 256 597
Affine transformation or mapping or motion, orthogonal projection 460 462 468 624 627 635
Affine transformation or mapping or motion, orthogonal projection, affinity 285
Affine transformation or mapping or motion, orthogonal projection, elliptic (orthogonal) rotation 283
Affine transformation or mapping or motion, orthogonal projection, hyperbolic (orthogonal) rotation 283
Affine transformation or mapping or motion, orthogonal reflection 274 461 624
Affine transformation or mapping or motion, reflection (skew) 251 591
Affine transformation or mapping or motion, reflection (skew), orthogonal reflection 253 274 592 624
Affine transformation or mapping or motion, reflection (skew), symmetric motion 253 592
Affine transformation or mapping or motion, regular or proper or nonsingular 251 655
Affine transformation or mapping or motion, rotation 271 272 620
Affine transformation or mapping or motion, shearing 265 266 611 612 613
Affine transformation or mapping or motion, shearing, skew shearing 282 635
Affine transformation or mapping or motion, singular 251
Affine transformation or mapping or motion, the fundamental theorem 241 580
Affine transformation or mapping or motion, translation 67 247 251 591
Affine transformation or mapping or motion, two-way stretch 261 604
Affine transformation or mapping or motion, two-way stretch, enlargement (scale factor) 262 605
Affine transformation or mapping or motion, two-way stretch, orthogonal two-way stretch 261
Affine, natural affine basis for 239
Affine, natural affine basis for 581
Algebra homomorphism 744
Algebra isomorphism 119 406
Algebraic rank (of a matrix) 125 367 383 407 739
Annihilator 213 214 421 752 757 802
Area coordinate 76
Area coordinate, affine coordinate system 76
Area coordinate, affine coordinate system base point 76
Area coordinate, affine coordinate system base triangle 76
Area coordinate, affine coordinate system vertex 76
Area coordinate, barycentric coordinate 76
Area coordinate, base point 76
Area coordinate, coordinate or base triangle 76
Area coordinate, homogeneous area coordinate 76
Area coordinate, ideal or infinite point 76
Area coordinate, normalized barycentric coordinate 76
Area coordinate, oriented triangle 75
Area coordinate, oriented triangle, signed area 75
Area coordinate, orthogonal or Descartesian or rectangular coordinate system 77
Area coordinate, signed distance 78
Augmented matrix 150 152 156 180 377 416 425 724
Barycentric coordinate for (a line) 19
Barycentric coordinate for (a line)barycenter (middle point of base segment) 19
Barycentric coordinate for (a plane) 72
Barycentric coordinate for (a plane), affine coordinate 72
Barycentric coordinate for (a plane), barycenter (of base triangle) 72
Barycentric coordinate for (a plane), base triangle 72
Barycentric coordinate for (a space) 363 642
Barycentric coordinate for (a space), affine coordinate 363
Barycentric coordinate for (a space), barycenter (of base tetrahedron) 363 642
Barycentric coordinate for (a space), base tetrahedron 363
Barycentric coordinate for (a space), coordinate axis 363
Barycentric coordinate for (a space), coordinate plane 363
Basis 9 10 31 34 71 324 326 330 336 697
Basis, basis vectors 9 10 31 34 71 324 326 697
Basis, changes of bases (coordinates) 16 46 117 337 406 735
Basis, natural or standard (orthonormal) basis for 38 55
Basis, natural or standard (orthonormal) basis for 328 335 366
Basis, natural or standard basis for 693 697
Basis, ordered basis 9 10 34 324 326 331 698
Basis, Steinitz's replacement theorem 697
Bessel inequality 779
Bilinear form 304 756
Block or partitioned matrix 180
Block or partitioned matrix addition 181
Block or partitioned matrix conjugate transpose 181
Block or partitioned matrix Frobenius inequality (for ranks) 186
Block or partitioned matrix of the same type 181
Block or partitioned matrix product 181
Block or partitioned matrix rank decomposition theorem (of a matrix) 184
Block or partitioned matrix scalar multiplication 181
Block or partitioned matrix Schur's formula 182
Block or partitioned matrix Sylvester inequality (for ranks) 186
Block or partitioned matrix transpose 181
Block or partitioned matrix, pseudo-diagonal, lower or upper triangular 181
Block or partitioned matrix, submatrix 134 180
Canonical form (of a matrix) 559
Canonical form (of a matrix), canonical form of real matrices under similarity 399
Canonical form (of a matrix), canonical or standard form of quadratic curves 303
Canonical form (of a matrix), canonical or standard form of quadrics: Euclidean, affine, projective 670 675 679
Canonical form (of a matrix), diagonal canonical form (of a square matrix) 193 198 386 399 479 718 797
Canonical form (of a matrix), Jordan canonical form (of a square matrix) 222 224 393 395 399 516 541 543 547—552 799 805
Canonical form (of a matrix), rational canonical form (of a square matrix) 233 390 398 399 560 562 574 809 812
Cauchy — Schwarz inequality 774
Cayley — Hamilton theorem 108 209 213 221 399 402 477 792
Ceva theorem 291 296 651
Change of coordinates 16 46 337
Change of coordinates formula 16 46 337
Change of coordinates, transition matrix or change of coordinates matrix 16 46 337 735
Characteristic equation 106 384 719 791
Characteristic of a field 686
Characteristic polynomial (of a linear operator or square matrix) 106 193 212 384 407 491 719 791 795
Characteristic root (eigenvalue) 105 384 407 719 790
Characteristic vector (eigenvector) 105 384 407 719 790
Co-dimension 747
| Coefficient matrix 56 149 152 156 250 342 377 416 425 442
Column rank (of a matrix) 125 366 367 383 407
Column space 125 407 757
Column vector 125 367 375 703
Complete quadrilateral 299
Complete quadrilateral cross ratio 299 300 661
Complete quadrilateral harmonic points 299 300
Complete quadrilateral signed ratio 299
Congruence of matrix 166 454
Congruence of matrix, Sylvester's law of inertia (of symmetric bilinear form or symmetric matrix) 166 454
conic 300 306
Conic, center 306
Conic, central 306
Conic, degenerated 306
Conic, noncentral 306
Conic, nondegenerated 306
Conjugate (matrix) of a matrix 702
Conjugate (matrix) of a matrix, conjugate transpose 702 714
Convex set 653
Convex set, convex cell 653
Convex set, convex hull or closure 653
Coordinate system (also called affine basis) 9 10 31 34 46 324
Coordinate system (also called affine basis) (associated) vector space 9 10 31 34 324 326
Coordinate system (also called affine basis) affine or oblique coordinate system 38 328
Coordinate system (also called affine basis) basis (vector) 9 31 324
Coordinate system (also called affine basis) Cartesian or rectangular or natural coordinate system 38 328 335
Coordinate system (also called affine basis) origin 9 31 324
Coordinate system (also called affine basis) zero vector 9 31 324
Coordinate vector (of a point or a vector w. r. t. a basis) in 10
Coordinate vector (of a point or a vector w. r. t. a basis) in (first, second component) 34
Coordinate vector (of a point or a vector w. r. t. a basis) in (first, second, third component) 326
Coordinatized space (w. r. t. an affine basis) of a (three-dimensional) space 326
Coordinatized space (w. r. t. an affine basis) of a plane 35
Coordinatized space (w. r. t. an affine basis) of a straight line 11
Cross ratio (of four points) 300 661
Darboux theorem 291
Decomposition of matrices LU, LDU, LDL*, LPU, LS 161 162 167 442
Decomposition of matrices, lower and upper triangular decomposition (of a square matrix) 161
Decomposition of matrices, polar decomposition 772
Decomposition of matrices, rank decomposition theorem (of a matrix) 184
Decomposition of matrices, singular value decomposition theorem (SVD) 178 771
Desargues theorem 296
Determinant 727
Determinant adjoint matrix of a square matrix 731
Determinant cofactor 728 730
Determinant Cramer's rule 88 732
Determinant expansion along a row or a column 728
Determinant inverse matrix of an invertible matrix 731
Determinant Laplace expansion 730
Determinant minor 728
Determinant properties 728
Determinant, real determinant of order 2 47 55 106 121
Determinant, real determinant of order 3 336 337
Determinant, real determinant of order 3, adjoint matrix 336 731
Determinant, real determinant of order 3, cofactor 336
Determinant, real determinant of order 3, expansion along a row or a column 336
Determinant, real determinant of order 3, minor 336
Determinant, subdeterminant 730
Determinant, subdeterminant principal 730
Diagonalizable linear operator or matrix 117 193 198 212 385 399 479 718 794
Diagonalizable linear operator or matrix, characteristic polynomial (equation) 106 121 193 198 216 407 437 719 791 795
Diagonalizable linear operator or matrix, criteria for diagonalizability 198 212 479 718 796
Diagonalizable linear operator or matrix, criteria for diagonalizability, algebraic multiplicity 199 479 797
Diagonalizable linear operator or matrix, criteria for diagonalizability, geometric multiplicity 199 479 797
Diagonalizable linear operator or matrix, diagonal canonical form or decomposition (of a square matrix or linear operator) 199 479 797
Diagonalizable linear operator or matrix, eigenspace 193 198 478 791
Diagonalizable linear operator or matrix, eigenvalue or characteristic value (root) 105 106 190 193 198 385 477 719 790
Diagonalizable linear operator or matrix, eigenvector or characteristic vector 105 106 121 190 193 198 385 477 719 790
Diagonalizable linear operator or matrix, generalized eigenspace 210 224 516 794 801
Diagonalizable linear operator or matrix, generalized eigenvector 224 516 794
Diagonalizable linear operator or matrix, minimal polynomial 199 209 214 479 794 795
Diagonalizable linear operator or matrix, simultaneously diagonalizable 209 213
Differential equation 505
Differential equation, homogeneous 505
Differential equation, linear ODE with constant coefficients 509
Differential equation, nonhomogeneous 508 552
Dimension (of a vector space) 12 36 43 327 330 698
Dimension (of a vector space), dimension theorem 88 366 734 738
Dimension (of a vector space), finite-dimensional 697
Dimension (of a vector space), infinite-dimensional 697
Dimension (of a vector space), n-dimensional 698
Direct sum of restriction operators 210 211
Direct sum of subspaces 33 41 330 694 746
Directed (line) segment 6 7 65 356
Directed (line) segment coordinate or parametric representation 18 61 62 356
Directed (line) segment end point 18 65 356
Directed (line) segment exterior point 18 65 356
Directed (line) segment initial point 18 65 356
Directed (line) segment interior point 18 65 356
Directed (line) segment length 6
Directed (line) segment middle point 19 65 356
Directed (line) segment negative direction 6
Directed (line) segment positive direction 6
Directed (line) segment signed length 6
Directed (line) segment terminal point 18 65 356
Discriminant of a quadratic curve 306
Discriminant of a quadratic equation 689
Discriminant of a quadric 679
Dual basis 420 750
Dual space 420 749
Dual space, second 421 751
Echelon matrix 164 443 721
Echelon matrix, leading entry of a row (of a matrix) 721
Echelon matrix, pivot 162 164 721
Echelon matrix, pivot, free variable 721
Echelon matrix, pivot, pivot column (or row) 164 721
Echelon matrix, pivot, pivot matrix 162
Echelon matrix, pivot, pivot variable 721
Echelon matrix, row-reduced echelon matrix 164 443 721
Eigenspace 193 210 224 478 479 516 791 794
Eigenvalue (characteristic value, root) 105 190 193 224 384 477 479 516 719 794
Eigenvector (characteristic vector) 105 190 193 224 384 477 479 516 719 791
Elementary column or row operation 149 150 442 719
Elementary column or row operation, type 1 149 150 442 719 720
Elementary column or row operation, type 2 149 150 442 719 720
Elementary column or row operation, type 3 149 150 442 719 720
Elementary divisor 804
Elementary matrix 150 442 720
Elementary matrix, elementary matrix factorization (of an invertible matrix) 161 444 726
Elementary symmetric function (of n variables) 491
Elimination method 148 442 719
ellipse 303 304 305
Ellipse, imaginary ellipse 303 305
Ellipsoid 670
Ellipsoid, elliptic cone 670
Ellipsoid, elliptic cylinder 671
Ellipsoid, elliptic paraboloid 670
Ellipsoid, imaginary ellipsoid 670
Ellipsoid, imaginary elliptic cylinder 671
Ellipsoid, point ellipsoid 670
Elliptic rotation 312 313
Elliptic rotation, transitive one-parameter subgroup of 313
Enlargement: scale, invariant point 95 247 262 385 611
f-cyclic subspace generated by a vector 209 210 802
f-invariant subspace 210
Field 684
Field characteristic 686
Field, complex () 685
Field, finite field () 686
Field, infinite field 686
Field, rational () 686
Field, real () 685
Finite-dimensional vector space 697
Free variable 721
Function 682
Function composite 683
Function identity 683
Function, domain, range 682
Function, equal 682
Function, image, preimage 682
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