A.3.4 Vector products, 447
A.3.5 Index notation, 448
A.3.6 Vector spaces, 449
A.4 Matrix algebra, 450
A.4.1 Definitions, 450
A.4.2 Determinant, 451
A.4.3 Inverse, 452
A.4.4 Systems of linear equations, 452
A.4.5 Solving systems of equations on
a computer, 453
A.5 Vector transformations, 454
A.5.1 Coordinate transformations, 455
A.5.2 Eigenvalues and eigenvectors, 456
A.5.3 Symmetric matrix eigenvalues, eigenvectors,
diagonalization, and decomposition, 458
A.6 Vector calculus, 458
A.6.1 Scalar and vector fields, 458
A.6.2 Gradient, 459
A.6.3 Divergence, 459
viii Contents
A.6.4 Curl, 460
A.6.5 Laplacian, 461
A.7 Spherical coordinates, 462
A.7.1 The spherical coordinate system, 462
A.7.2 Distance and azimuth, 463
A.7.3 Choice of axes, 465
A.7.4 Vector operators in spherical coordinates, 465
A.8 Scientific programming, 466
A.8.1 Example: synthetic seismogram calculation, 466
A.8.2 Programming style, 469
A.8.3 Representation of numbers, 470
A.8.4 A few pitfalls, 471
A.8.5 Some philosophical points, 472
Further reading, 473
Problems, 473
References, 476
Solutions to selected odd-numbered problems, 486
Index, 489