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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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Graphics standards, GKS 298 Graphics standards, OpenGL 233 Grassmann, H. 61 Homogeneous 31 Homogeneous coordinates 233 Homogeneous linear system 100 127 Homogeneous linear system, unsolvable 100 Homogeneous property 170 Horizontal tangent 326 Householder matrix 192 280 Hurricane 14 17 Hyperbola 156 159 Idempotent 73 80 131 Identity matrix 112 Ill-conditioned system 284 Illumination 177 Image of linear map 60 268 Implicit equation of a line 37 Implicit equation, conic 156 Incenter 146 incircle 146 Inclusion test 143 Inequality, Cauchy — Schwartz 29 Inequality, triangle 30 286 Inflection point 328 329 Inner product 25 271 276 Interior angle 300 301 Interpolation curve 321 Intersection, cone and plane 156 Intersection, line and plane 189 230 Intersection, planes 224 Intersection, three planes 193 Intersection, triangle and line 191 Intersection, two lines 48 88 173 Intersection, two planes 194 Inverse matrix 95 256 270 Inverse matrix, eigenvalues 273 Inverse matrix, identity 95 Inverse matrix, rotation 95 Inverse matrix, scale 95 Inverse, 2 93 Inverse, 3 219 Inverse, n 256 Involutary matrix 282 Iterative method, convergence 290 Iterative method, convergence rate 290 Iterative method, eigenvalue 290 Iterative method, Gauss — Jacobi 290 Iterative method, Gauss — Seidel 290 Iterative method, power method 290 Iterative method, residual vector 290 Kernel 131 Kernel, 2D map 74 Kernel, of a matrix 73 Lagrange’s identity 170 Law of Cosines 26 Least squares, approximation 132 Least squares, Householder method 284 Least squares, line fitting 255 Least squares, normal equations 254 Lighting model 177 LIMIT 285 Line, 2D 33 Line, 3D 172 Line, closest point 47 Line, convert implicit to parametric 41 Line, convert parametric to implicit 41 Line, distance between two 187 Line, distance of a point to 43 Line, explicit equation 40 Line, extrapolation 35 Line, implicit equation 37 172 Line, intersection with a triangle 191 Line, intersection with plane 230 Line, normal 37 Line, parallel 173 Line, parameter 35 Line, parametric equation 35 172 Line, parametric form 316 Line, parametrization 37 43 Line, perpendicular 173 Line, point normal form 37 45 Line, segment 22 Line, skew 172 187 Line, slope 40 linear combination 24 58 62 92 110 181 182 266 Linear independence 266 Linear independence, rank of a matrix 63 Linear interpolation 35 316 Linear map 200 268 Linear map, 2D 57 87 110 Linear map, 3D 201 224 Linear map, addition 62 Linear map, area 65 66 69 70 74 Linear map, commutative law 79 Linear map, composite 77 Linear map, condition number 137 Linear map, coordinates 60 Linear map, determinant 74 Linear map, diagonalizable 133 Linear map, distributive law 62 Linear map, eigenvalue 125 Linear map, eigenvalue analysis 125 Linear map, fixed direction 125 127 Linear map, idempotent 73 Linear map, ill-conditioned 138 Linear map, image 60 268 Linear map, inverse 95 138 Linear map, kernel 73 Linear map, linearly independent columns 63 Linear map, matrix form 59 Linear map, noncommutative 79 Linear map, preimage 268 Linear map, preserve linear combinations 62 Linear map, preserve scalings 61 Linear map, preserve summations 61 Linear map, projection 71 Linear map, rank, eigenvalue 131 Linear map, ratios 110 Linear map, reduce dimension 72 Linear map, reflection 65 Linear map, repeated 135 Linear map, rigid body motion 69 96 Linear map, rotation 68 Linear map, scaling 63 Linear map, shear 69 Linear map, symmetric 63 Linear map, transpose 62 Linear map, triangle 114 Linear map, volume 213 Linear map, well-conditioned 138 Linear space 15 166 181 Linear space, examples 274 Linear system 182 241 Linear system, 2 87 89 Linear system, 3 243 Linear system, augmented matrix 248 Linear system, back substitution 91 94 244 248 Linear system, CLAPACK 242 Linear system, coefficient matrix 243 Linear system, condition number 137 Linear system, consistent 89 100 243 Linear system, coordinate transformation 115 Linear system, Cramer’s Rule 90 Linear system, determinant 90 Linear system, elementary row operation 244 Linear system, forward substitution 260 361 Linear system, Gauss elimination 91 244 258 Linear system, Gauss — Jacobi iteration 289 Linear system, general 241 Linear system, geometry of a 2 89 Linear system, homogeneous 100 127 Linear system, Householder transformation 280 Linear system, ill-conditioned 284 Linear system, inconsistent 89 100 Linear system, infinite number of solutions 100 243 Linear system, iterative method 287 Linear system, large 287 Linear system, least squares solution 254 Linear system, matrix form 242 Linear system, no solution 243 Linear system, nontrivial solution 100 Linear system, numerical stability 91 138 Linear system, overdetermined 173 253 Linear system, pivoting 102 103 245 247 Linear system, solution 89 Linear system, solution space 89 Linear system, sparse 287 Linear system, trivial solution 100 Linear system, true solution 103 Linear system, underdetermined 100 Linear system, unique solution 243 Linear system, UNPACK 242 Linear system, unsolvable 99 Linear system, upper triangular 244 Linearly dependent 24 99 101 115 182 Linearly independent 24 63 91 182 195 257 266 LINPACK 242 Local coordinate system 104 329 Local coordinate system, 2D 3 Local coordinate system, 3D 8 Local coordinate system, barycentric coordinates 142 Local coordinate system, Frenet frame 329 Local coordinate system, Gram — Schmidt method 195 Lower triangular 259 LU decomposition 258 LU decomposition, inverse matrix 257 Manhattan norm 286 Map, affine 108 110 144 200 Map, general linear spaces 268 Map, linear 110 200 224 Map, perspective 207 234 Matrix 59 89 Matrix form, of B 323 Matrix form, of monomial curve 323 Matrix inverse, identity 95 Matrix inverse, rotation 95 Matrix inverse, scale 95 Matrix multiplication, 2D 81 Matrix multiplication, 3D 216 Matrix multiplication, composite maps 77 Matrix multiplication, manual computation 78 Matrix multiplication, non-commutivity 217 Matrix multiplication, properties 82 83 Matrix, 2D linear map 59 Matrix, 3D linear maps 200 Matrix, addition 62 Matrix, area 65 66 69 70 74 Matrix, associative law 83 Matrix, augmented matrix 248 Matrix, commutative law 79 83 Matrix, decomposition 160 Matrix, determinant 74 82 99 Matrix, diagonal 60 Matrix, diagonalizable 133 Matrix, diagonally dominant 290 Matrix, distributive law 62 83 Matrix, dyadic 192 231 281 Matrix, eigenvalue 131 Matrix, exponent 82 Matrix, factorization 259 Matrix, full rank 63 257 269 Matrix, Gauss 248 Matrix, general linear space 268 Matrix, Householder 192 Matrix, identity 94 Matrix, inverse 93 95 97 115 219 256 270 Matrix, invertible 99 Matrix, involutary 282 Matrix, kernel 73 101 131 Matrix, linear combination 62 Matrix, linear operation 61 Matrix, linearly independent columns 63 Matrix, LU decomposition 257 258 Matrix, multiplication 78 81 Matrix, nonsingular 99 324 Matrix, not invertible 99 Matrix, notation 59 Matrix, orthogonal 96 133 210 220 282 Matrix, positive definite 134 138 Matrix, preserve scalings 61 Matrix, preserve summations 61 Matrix, projection 71 125 207 229 Matrix, properties 62 201 218 Matrix, rank 63 72 231 250 257 268 Matrix, rank deficient 250 Matrix, reflection 65 204 Matrix, rigid body motion 69 96 112 212 225 Matrix, rotation 68 95 209 Matrix, scaling 63 94 202 Matrix, shear 69 204 Matrix, singular 99 257 Matrix, sparse 287 Matrix, square 269 Matrix, symmetric 63 138 282 Matrix, symmetric part 135 Matrix, transpose 62 81 201 Matrix, unit 94 Matrix, unitary 282 Matrix, upper triangular 91 244 247 Matrix, zero 258 Median of a triangle 145 midpoint 16 Minmax box 300 310 323 Minor 213 252 Moebius, F. 142 Monomial, convert to B 323 Monomial, geometric interpretation 324 Monomial, polynomials 323 Multiplier 248 NDC coordinates 121 NETLIB 242 Non-associative property, cross product 170 Norm, 286 Norm, Euclidean 286 Norm, Manhattan 286 Norm, vector 285 normal 153 Normal, for computer graphics 177 Normal, vertex 180 Normalized coordinates 6 Normalized device coordinates 12 Numerical stability 91 102 309 Numerical stability, round-off 103 Oblique projection 230 Orientation 178 Orthogonal, coordinate frame 10 Orthogonal, eigenvectors 132 Orthogonal, Matrix 133 210 282 Orthogonal, projection 29 Orthogonal, projection, Gram-Schmidt 195 Orthogonal, vectors 132 271 Orthographic projection 229 Orthonormal 96 168 210 220 Orthonormal basis 271 Orthonormal, Gram — Schmidt 195 271 Osculating plane 330 Overdetermined linear system 253 284 parabola 156 159 Parallel, lines 111
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