Linear Algebra

Indexaccuracyof Gauss’s Method, 65–68rounding error, 66adding rows, 4additionvector, 76additive inverse, 76adjoint matrix, 328angle, 42antipodal, 345antisymmetric matrix, 135argument, A-8arrow diagram, 215, 230, 236, 240, 358augmented matrix, 14automorphism, 161dilation, 161reflection, 161rotation, 161back-substitution, 5base stepof induction, A-5basis, 109–120change of, 236definition, 109orthogonal, 254orthogonalization, 254orthonormal, 255standard, 110, 357standard over the complex numbers,357string, 379best fit line, 267block matrix, 312box, 320orientation, 322sense, 322volume, 322C language, 65canonical formfor matrix equivalence, 243for nilpotent matrices, 382for row equivalence, 55for similarity, 401canonical representative, A-11Cauchy-Schwartz Inequality, 42Cayley-Hamilton theorem, 390central projection, 341change of basis, 236–247characteristicvectors, values, 364characteristic equation, 368characteristic polynomial, 368satisfied by, 392characteristic root, 372characterized, 170characterizes, 245Chemistry problem, 1, 9chemistry problem, 22Chiò’s formula, 338Chiò’s Method, 337Chiò’s method, 340circuitsparallel, 70series, 70series-parallel, 71classequivalence, A-11closure, 91of null space, 375of range space, 375codomain, A-8cofactor, 327column, 13rank, 122vector, 14