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Farin G., Hansford D. — Practical Linear Algebra: A Geometry Toolbox
Farin G., Hansford D. — Practical Linear Algebra: A Geometry Toolbox

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Название: Practical Linear Algebra: A Geometry Toolbox

Авторы: 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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 384

Добавлена в каталог: 29.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L^{2}$ norm      286
$L^{A}T_{E}X$      2 341
Acceleration      326
Accuracy      143
Affine invariance      144
Affine invariance, barycentric coordinates      144
Affine invariant      92
Affine invariant, B$\acute{e}$zier curve      321
Affine map      108 144 162 200 321
Affine map, 2D      110
Affine map, 3D      224
Affine map, B$\acute{e}$zier curve      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$\acute{e}$zier curve      315 316
B$\acute{e}$zier curve, affine invariant      321
B$\acute{e}$zier curve, composite      326
B$\acute{e}$zier curve, convert to monomial      323
B$\acute{e}$zier curve, convex hull property      322
B$\acute{e}$zier curve, curvature      327
B$\acute{e}$zier curve, de Casteljau algorithm      317
B$\acute{e}$zier curve, derivative      324
B$\acute{e}$zier curve, evaluation      317
B$\acute{e}$zier curve, extrapolation      323
B$\acute{e}$zier curve, inflection point      328
B$\acute{e}$zier curve, robot motion      331
B$\acute{e}$zier curve, second derivative      326
B$\acute{e}$zier curve, subdivision      321
B$\acute{e}$zier points      316
B$\acute{e}$zier polygon      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 $\times$ 4 matrix      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$\acute{e}$zier curve to monomial curve      323
Convert, degrees to radians      28
Convert, implicit to parametric line      41
Convert, monomial curve to B$\acute{e}$zier curve      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, $[a_{1},a_{2},a_{3}]$      200 224
Coordinate system, $[e_{1},e_{2},e_{3}]$      8 224
Coordinate system, $[e_{1},e_{2}]$      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 $\times$ 2      90
Cramer’s rule, 3 $\times$ 3      253
Cramer’s rule, n $\times$ 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$\acute{e}$zier      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$\ddot{u}$rer, A.      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 $\times$ 2 matrix      75
Determinant, 3 $\times$ 3 matrix      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 $\times$ 2      123
Eigen things, n $\times$ 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 $\times$ n system      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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