INDEX 513

block diagonal, 91block multiplication, 89commuting, 360invertible, 95notation, 77rotation, 111transpose, 80

matrix, 77differentiation operator, 105inverse, 81left inverse, 180linear transformation, 104lower triangular, 181main diagonal, 135Markov, 285polynomial, 191right inverse, 180right, left inverse, 180row, column, determinant rank, 183stochastic, 285upper triangular, 181

matrixpositive definite, 386

matrix exponential, 405matrix multiplication, 78

properties, 80maximal chain, 503maximal ideal, 67maximum likelihood estimates

covariance, 356mean, 356

Mayer Vietorissequence, 480

mean value theoremCauchy, 447

metric, 245properties, 245

metric space, 245compact sets, 253complete, 248completely separable, 252open set, 245separable, 252

metric tensor, 319migration matrix, 289minimal polynomial

finding it, 165minimum polynomial, 69, 127

algebraic number, 69direct sum, 160finding it, 129

minor, 178module, 152

cyclical, 153direct sum, 154Noetherian, 153

monomorphism, 152, 211Moore Penrose inverse, 377

least squares, 378uniqueness, 385

morphism, 152multivariate normal distribution, 355Muntz theorems, 453

negative definite, 370Neuman

series, 410nilpotent, 144non solvable group, 234nondefective, 135norm

p norm, 268strictly convex, 403uniformly convex, 403

normal closure, 237normal extension, 221normal matrix, 332normal subgroup, 222, 232null and rank, 325

open ball, 245open set, 245

open cover, 252open set, 245open sets

countable basis, 252operator norm, 274order, 17ordered

partial, 503totally ordered, 503

orthonormal, 270orthonormal basis

existence, 309orthonormal polynomials, 322

parallelepiped