INDEX 481

Newton, 26nilpotent, 123, 436non defective

minimal polynomial, 461nondefective, 297nondefective eigenvalue, 255normed linear space, 406normed vector space, 406null space, 170, 195nullity, 172

one to one, 187rank, 182

onto, 187open ball, 20operator norm, 339orthogonal complement, 413orthogonal matrix, 123, 199, 213, 289

switching two unit vectors, 213orthogonal projection, 410, 413orthogonality and minimization, 309orthonormal, 290, 304

independent, 406orthonormal set, 406

p norms, 344parallelepiped, 46

volume, 46parallelogram identity, 422particular solution, 194partitioned matrix, 301permutation, 130permutation matrices, 143permutation symbol, 48

reduction identity, 49perp, 173perpendicular, 34pivot, 65pivot column, 59, 149pivot columns, 60pivot position, 59pivot positions, 60PLU factorization, 211points and vectors, 15polar form complex number, 6polarization identity, 422polynomial, 383

degree, 383

divides, 384division, 383equal, 383greatest common divisor, 384greatest common divisor, uniqueness,

384irreducible, 384irreducible factorization, 385relatively prime, 384root, 383

polynomialmatrix coefficients, 141

polynomialscanceling, 386factoring, 8factorization, 386

position vector, 18power method, 347preserving distance, 315principal axes, 300principal directions, 268product of matrices

composition, 446projection, 36, 179projection of a vector, 36projections

matrix, 192

QR decomposition, 305QR factorization, 214, 305

thin, 305quadratic form, 300quadratic formula, 9

rankcolumn determinant and row, 155existence of solutions, 173finding the rank, 157linear transformation, 444

rank and singular values, 318rank of a matrix, 155, 175Rayleigh quotient, 357reflection

across a given vector, 199regression line, 312regular Sturm Liouville problem, 418resultant, 26right handed system, 41