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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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Parallel, planes 224 Parallel, projection 207 Parallel, vectors 170 Parallelepiped 180 204 213 270 Parallelogram rule 16 Parallelogram rule, second derivative 326 PARAMETER 3 23 35 Parametric curve 316 Parametric equation of a line 35 Parametrization 37 43 316 Perpendicular distance 174 Perspective map, properties 235 Perspective projection 234 Phong illumination model 177 Piecewise B 326 Pivoting 102 215 245 280 Pixel 6 40 Plane 156 Plane, bisector of two points 177 Plane, definition 168 173 Plane, distance to a point 174 186 Plane, distance to origin 174 Plane, Euclidean definition 177 Plane, family 176 Plane, implicit form 173 Plane, intersection, of three planes 193 Plane, intersection, of two planes 194 Plane, intersection, with line 230 Plane, normal 173 Plane, parallel to another 224 Plane, parametric form 176 Plane, plane, intersecting 224 Plane, point normal equation 173 Point 14 166 Point cloud 11 Point location algorithm 150 Point, 2D 14 Point, affine map 108 Point, barycentric combination 111 Point, closest on a line 114 Point, combination 21 Point, distance to a plane 174 186 Polygon fill algorithm 40 Polygon, area 305 Polygon, circle approximation 302 Polygon, clipping 300 Polygon, concave 300 Polygon, convex 300 Polygon, cyclic numbering 300 Polygon, definition 299 Polygon, equiangular 302 Polygon, equilateral 302 Polygon, even-odd rule 311 Polygon, exterior angle 300 304 Polygon, inside/outside test 310 Polygon, interior angle 300 Polygon, into an Escher-style figure 298 Polygon, n-gon 302 Polygon, nonsimple 302 Polygon, planarity 309 Polygon, rectangle 302 Polygon, regular 302 Polygon, rhombus 302 Polygon, simple 302 Polygon, sum of interior angles 301 Polygon, total turning angle 305 Polygon, turning angle 300 304 Polygon, visibility test 310 Polygon, winding number 305 312 Polygon, with a hole 303 Polygonal mesh 300 Polyline, definition 298 Polyline, graphics standards 298 Polyline, winding number 312 Polynomial 274 Polynomial, B 319 Polynomial, Bernstein 320 Polynomial, monomial 320 Positive definite 134 PostScript 2 333 PostScript, matrix 121 PostScript, polygon fill 310 PostScript, tutorial 333 Power method 290 Preimage 268 Projection 271 Projection, 2D 71 101 131 Projection, 3D 207 229 Projection, area 73 Projection, oblique 229 Projection, orthogonal 29 229 Projection, parallel 71 207 Projection, perspective 207 234 Projection, volume 208 Projective maps 235 Pythagorean Theorem 18 25 166 Quadratic equation 125 Quadratic polynomial 276 Quadratic polynomial, zeroes 129 RADIANS 27 28 301 RANGE 268 Rank 63 72 131 250 257 268 Rank deficient 250 ratio 3 22 110 111 224 Ratio, area 142 144 Ratio, aspect 5 Ratio, condition number 138 Ratio, perspective map 235 Ray, polygon intersection 311 Ray, tracing 186 189 Real space 15 Reflection 76 113 Reflection, 2D 65 Reflection, 3D 204 Reflection, area 66 Reflection, Householder matrix 192 280 Reflection, line and plane 191 Reflection, volume 204 Residual vector 290 Rhombus 302 Right-hand rule 76 134 168 178 210 Right-hand rule, cross product 170 Rigid body motion 69 96 112 212 225 Robot motion 331 Rotation 95 Rotation, 2D 68 Rotation, 3D 209 Rotation, area 69 Rotation, conic 163 Rotation, eigenvector 129 Rotation, right-hand rule 210 Rotation, volume 212 Round-off 28 103 Row echelon form 250 Rubberband test 300 Satellite data 148 scalar 14 167 Scalar product 25 Scalar triple product 180 213 305 307 Scaling 94 Scaling, area 65 Scaling, volume 203 Screen coordinates 6 Second derivative 326 SEQUENCE 285 Shading 153 177 Shear 75 92 250 Shear, 2D 69 Shear, 3D 204 Shear, area 70 Shear, determinant 213 Shear, eigenvector 130 Shear, Gauss elimination 244 280 Shear, volume 207 Significant digits 282 Singular matrix 257 Singular value 138 Singular value decomposition 138 Skew box 204 Skew lines 187 Space, Euclidean 14 166 Space, linear 15 166 Space, real 15 166 Space, vector 15 166 span 182 266 sparse 287 Sphere 167 Square matrix 269 Star 148 180 Subdivision, of B 321 subspace 168 182 243 surface 299 Surface, trimmed 304 Symmetric matrix 125 282 Symmetric matrix, application 132 Symmetric matrix, conic 158 Symmetric matrix, diagonalizable 133 Symmetric matrix, geometry 132 Symmetric matrix, orthogonal eigenvectors 132 Symmetric matrix, real eigenvalue 131 273 Symmetric matrix, reflection vector 192 Symmetry property 170 Tacoma Narrows bridge 124 Tangent 325 326 Target box 3 58 Target box, skew 58 88 108 tetrahedron 224 225 243 Tin 148 Tolerance, angle 50 Tolerance, barycentric coordinate 143 Tolerance, distance 38 Tolerance, floating point accuracy 143 Tolerance, meaningful 38 309 Tolerance, zero divide 19 Total turning angle 305 Translation 108 111 Translation, 3D 225 Translation, conic 162 Translation, rigid body motion 112 TRANSPOSE 81 Transpose matrix, 2D 62 Transpose matrix, eigenvalues 273 Transpose, vector 63 triangle 30 114 300 Triangle inequality 30 286 Triangle, area 142 146 Triangle, barycentric coordinates 191 Triangle, centroid 145 Triangle, circumcenter 146 Triangle, circumcircle 146 Triangle, circumference 146 Triangle, incenter 146 Triangle, inclusion test 143 151 Triangle, intersection with a line 191 Triangle, median 145 Triangle, special points 145 Triangle, vertex 142 Triangulation, 2D 148 Triangulation, 3D 151 Triangulation, boundary 150 Triangulation, coherence 151 Triangulation, data structure 149 Triangulation, Delaunay 149 Triangulation, neighbor information 150 151 Triangulation, point location algorithm 150 Triangulation, polygon area 305 Triangulation, sample file 154 Triangulation, star 148 180 Triangulation, uniqueness 149 Triangulation, valence 148 Trimmed surface, visibility test 310 Trimmed surface, visible region 304 Trivial reject 310 Trivial, solution 100 Turning angle 300 304 Unit cube 203 Unit matrix 94 Unit square 3 Unit vector 19 167 Unitary matrix 282 Valence 148 Vector 14 Vector field 17 Vector norm 285 Vector norm, 286 Vector sequence 285 Vector sequence, Gauss Jacobi iteration 288 Vector sequence, Gauss Seidel iteration 290 Vector sequence, power method 291 Vector space 15 181 Vector, 2D 15 Vector, 3D 166 Vector, cross product 168 177 Vector, dot product 25 167 Vector, inner product 25 Vector, Lagrange’s identity 170 Vector, left-handed 76 Vector, length 15 18 167 271 Vector, linearly dependent 115 Vector, magnitude 18 Vector, normalized 19 167 Vector, orthogonal 132 Vector, orthonormal 96 168 Vector, parallelogram rule 16 Vector, perpendicular 25 Vector, product 168 Vector, right-handed 76 Vector, scalar product 25 Vector, scaling 16 Vector, transpose 63 Vector, unit 19 167 Vector, zero 166 Velocity vector 326 Vertex normal 180 Vertex, of a triangle 142 Viewing volume 235 VIEWPORT 12 121 Volume 180 250 Volume, scalar product 213 Volume, Signed 180 Winding number 305 Winged-edge data structure 150 Wright, Prank Lloyd 33 Zero divide tolerance 19 Zero vector 15 72 100 166 266 299
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