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Farin G., Hansford D. — Practical Linear Algebra: A Geometry Toolbox
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Название: Practical Linear Algebra: A Geometry ToolboxАвторы: Farin G., Hansford D. Аннотация: Practical Linear Algebra introduces students in mathematics, science, engineering, and computer science to Linear Algebra from an intuitive and geometric viewpoint, creating a level of understanding that goes far beyond mere matrix manipulations. Practical aspects, such as computer graphics topics and numerical strategies, are covered throughout, and thus students can build a "Geometry Toolbox," based on a geometric understanding of the key concepts." This book covers all the standard linear algebra material for a first-year course; the authors teach by motivation, illustration, and example rather than by using a theorem/proof style.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2005Количество страниц: 384Добавлена в каталог: 29.11.2009Операции: Положить на полку |
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286 2 341 Acceleration 326 Accuracy 143 Affine invariance 144 Affine invariance, barycentric coordinates 144 Affine invariant 92 Affine invariant, B 321 Affine map 108 144 162 200 321 Affine map, 2D 110 Affine map, 3D 224 Affine map, B 321 Affine map, compose 116 Affine map, construction 112 Affine map, in terms of homogeneous coordinates 233 Affine map, projection 110 229 Affine map, properties 110 111 224 Affine map, ratio 110 Affine map, reflection 110 Affine map, rotation 110 Affine map, scale 110 Affine map, shear 110 Affine map, tetrahedra 225 Affine map, translation 108 112 225 Affine map, triangle 114 Angle bisector 146 192 Angle, cosine of 26 Angle, re-entrant 301 Angle, sine of 169 Anti-symmetry property cross product 170 Approximation, fitting lines 255 Approximation,least squares 254 Approximation,overdetermined linear system 254 Area 74 142 146 213 Area, parallelogram 90 168 213 Area, signed 143 Aspect ratio 5 Associative law 83 170 219 B 315 316 B 321 B 326 B 323 B 322 B 327 B 317 B 324 B 317 B 323 B 328 B 331 B 326 B 321 B 316 B 316 Back substitution 91 94 248 Barycenter 301 Barycentric combination 21 35 111 142 224 226 321 Barycentric coordinates 21 23 35 142 177 191 226 Barycentric coordinates, shading model 178 Basis 266 Basis function, Bernstein 319 Basis function, monomials 320 Basis vectors 24 Basis,orthonormal 271 Bernstein polynomial 319 Bisector, angle 146 192 Bisector, edge 146 Bisector, two points 177 Bisector, vector 192 Box, skew 204 Box, source 338 Box, target 338 Bresenham’s line drawing algorithm 40 Cauchy-Schwartz inequality 29 Center of gravity 22 Centroid 145 238 Centroid, of a tetrahedron 224 Characteristic equation 125 161 Characteristic polynomial 125 272 circle 156 Circle, approximation 302 Circle, incircle 146 Circumcenter 146 circumcircle 146 CLAPACK 242 CMM 10 Cofactor 213 252 Coherence 151 Collinear 327 Collinear points 110 Commutative law 83 219 Composite curves 326 Computer aided geometric design 11 315 Computer graphics 207 Computer graphics, 4 233 Computer graphics, affine map 232 Computer graphics, back-facing triangle 180 Computer graphics, Bresenham’s algorithm 40 Computer graphics, clipping algorithm 303 Computer graphics, culling 180 Computer graphics, flat shading 178 Computer graphics, flight simulator 200 Computer graphics, GKS 298 Computer graphics, Gouraud shading 178 Computer graphics, icons 6 Computer graphics, lighting model 177 Computer graphics, OpenGL 233 Computer graphics, Phong illumination model 177 Computer graphics, polygon clipping 300 Computer graphics, polygon fill 40 Computer graphics, ray tracing 186 189 Computer graphics, rotation 220 Computer graphics, shading 153 Computer graphics, smooth shading 178 Computer graphics, specular reflection 192 Computer graphics, viewing volume 235 Computer graphics, window 6 Condition number 137 138 Condition number, Gauss elimination 280 Condition number, Householder method 280 Cone 156 conic 155 Conic section 132 155 Conic, affine map 162 Conic, center 156 Conic, degenerate 160 Conic, general position 156 Conic, implicit equation 156 Conic, major axis 156 Conic, matrix notation 157 Conic, minor axis 156 Conic, position 162 Conic, standard position 156 Conic, symmetric matrix 158 Conic, type 160 Continuity conditions 327 Convergence, iterative method 290 Convergence, power method 291 Convert, B 323 Convert, degrees to radians 28 Convert, implicit to parametric line 41 Convert, monomial curve to B 323 Convert, parametric to implicit line 41 Convert, plane to point normal form 175 Convex combination 22 35 323 Convex hull 148 323 Convex hull, property 322 Coordinate frame 168 Coordinate independent 16 Coordinate measuring machine 10 Coordinate system 2 172 Coordinate system, 200 224 Coordinate system, 8 224 Coordinate system, 3 Coordinate system, global 2 Coordinate system, local 2 Coordinate transformation 108 Coordinate transformation, triangle to triangle 114 Coordinates, barycentric 21 142 Coordinates, global 2 Coordinates, homogeneous 233 Coordinates, local 2 Coordinates, map 60 Coordinates, normalized 6 Coordinates, screen 6 7 Coplanar 181 Cramer’s rule, 2 90 Cramer’s rule, 3 253 Cramer’s rule, n 252 Cross product 168 177 Cross product, barycentric coordinate 143 Cross product, properties 170 Cross section 14 CTM 338 341 Culling 180 Curvature, of planar curve 327 Curvature, signed 328 Curve 315 Curve, B 316 Curve, composite 326 Curve, continuity 327 Curve, derivative 324 Curve, evaluation 316 Curve, inflection point 328 Curve, monomial 323 Curve, parametric 316 Curve, second derivative 326 Curve, tangent 325 326 Cyclic numbering 300 Cyclic permutations 181 D 237 Data fitting 255 de Casteljau algorithm 317 De Casteljau algorithm, derivative 325 Delaunay triangulation 149 Derivative 274 324 Derivative, second 326 Descartes, R. 2 Determinant 74 90 115 125 169 213 250 270 328 Determinant, 2 75 Determinant, 3 181 213 Determinant, barycentric coordinate 143 Determinant, cofactor 213 252 Determinant, cyclic permutations 181 Determinant, geometric derivation 75 Determinant, matrix product 82 Determinant, minor 213 252 Determinant, orthogonal matrix 96 Determinant, polygon area 306 Determinant, scalar triple product 180 213 Determinant, symmetric matrix 135 Determinant, upper triangular matrix 251 Determinant, volume 181 213 Diagonalizable 133 Diagonally dominant 290 digitizing 10 Digitizing, local coordinate system 195 DIMENSION 182 266 Distance, between lines 187 Distance, between two points 20 Distance, perpendicular 174 Distance, point and plane 174 186 Distance, point to a line 43 Distance, signed 176 Distortion 5 Distributive law 61 62 Distributive law, cross product 170 Distributive law, dot product 31 Distributive law, matrices 83 219 Dominant eigenvalue 291 Dot product 25 81 167 216 Dyadic matrix 192 231 281 Eigen things, 2 123 Eigen things, n 272 Eigenvalue 125 160 Eigenvalue analysis 124 Eigenvalue, characteristic polynomial 272 Eigenvalue, conic 160 Eigenvalue, dominant 291 Eigenvalue, inverse matrix 273 Eigenvalue, power method 290 Eigenvalue, real value 131 Eigenvalue, repeated linear map 135 Eigenvalue, symmetric matrix 131 Eigenvalue, transpose matrix 273 Eigenvalue, zero 131 Eigenvector 125 127 Eigenvector, right-handed 134 Eigenvector, rotation matrix 129 Eigenvector, shear matrix 130 Elementary row operation 246 ellipse 156 158 Endpoint derivative 325 Equiangular polygon 302 Equilateral polygon 302 Escher, M.C. 119 298 Euclidean norm 286 Euclidean space 14 166 Expansion, by cofactors 252 Expansion, by minors 252 Explicit equation of a line 40 Exponent of a matrix 82 extents 6 300 Exterior angle 300 304 Extrapolation 35 323 Fallingwater 33 FEM 142 287 Finite precision machine 103 Fitting lines 255 Fixed direction 124 125 127 Fixed direction, rotation 129 Flat shading 178 flight simulator 199 Floating point accuracy 143 Font design 315 Foot of a point 47 114 186 Forward substitution 260 361 Frame of reference 172 Frenet frame 330 Full rank 63 162 257 269 Functional 275 Gauss elimination 91 193 206 244 261 269 270 Gauss elimination, algorithm 247 Gauss elimination, determinant 213 Gauss elimination, elementary row operation 246 Gauss elimination, failure of 91 Gauss elimination, multiplier 247 248 Gauss elimination, n 247 Gauss elimination, numerical problems 280 Gauss elimination, pivoting 102 245 Gauss elimination, row echelon form 250 Gauss matrix 248 Gauss — Jacobi iteration 289 Gauss — Seidel iteration 290 Geometric modeling 11 315 Gouraud shading 178 Grain — Schmidt 184 330 Grain — Schmidt, 3D 195 Grain — Schmidt, general linear spaces 271 Graphics standards 298
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