INDEX 407

Moore Penrose inverse, 318least squares, 318uniqueness, 323

moving coordinate system, 67acceleration , 70

negative definite, 304Neuman

series, 356nilpotent

block diagonal matrix, 245Jordan form, uniqueness, 245Jordan normal form, 245

non defective, 254nonnegative self adjoint

square root, 306norm, 273

strictly convex, 350uniformly convex, 350

normal, 311diagonalizable, 165non defective, 164

normed linear space, 273, 325normed vector space, 273norms

equivalent, 326null and rank, 288null space, 59nullity, 121

one to one, 10onto, 10operator norm, 328orthogonal matrix, 81, 89, 136, 162orthonormal basis, 275orthonormal polynomials, 285

p norms, 331axioms of a norm, 331

parallelepipedvolume, 288

partitioned matrix, 104Penrose conditions, 319permutation, 91

even, 113odd, 113

permutation matrices, 111perp, 122Perron’s theorem, 389pivot column, 119PLU factorization, 132

existence, 136

polar decompositionleft, 310right, 308

polar form complex number, 14polynomial, 25, 195

addition, 25degree, 25, 195divides, 196division, 25, 195equal, 195equality, 25greatest common divisor, 196uniqueness, 196description, 196

irreducible, 196irreducible factorization, 197multiplication, 25relatively prime, 196root, 195

polynomialleading coefficient, 195leading term, 25matrix coefficients, 110monic, 25, 195

polynomialscanceling, 197factorization, 198

positive definitepostitive eigenvalues, 304principle minors, 305

positive definite matrix, 323postitive definite, 304power method, 359prime number, 22prime numbers

infinity of primes, 211principal submatrix, 187principle directions, 151principle minors, 305product rule

matrices, 66projection map

convex set, 287

QR algorithm, 177, 371convergence, 374convergence theorem, 374non convergence, 178, 379

QR factorization, 137existence, 139Gram Schmidt procedure, 141