Principles of Mathematics in Operations Research

Index 295

unboundedness, 106, 251, 252

Markov process, 61, 87
matrix
asymmetric, 83
basis, 39
block diagonal, 58
column space, 26, 28, 44, 211-215
condition number, 82-86, 234-240
determinant, 51
diagonal, 21, 22, 43, 55, 56, 65, 226,
227
elementary, 21, 110
hermitian, 64
Hessenberg, 88
Hessian, 73, 231, 281
idempotent, 38
identity, 52
incidence, 28
Jordan form, 65, 226
left null space, 27, 28, 44, 211-215
minor, 53
multiplication, 17
nonsingular, 74
norm, 84-86, 234-240
normal, 65
null space, 26, 28, 44, 54, 57, 211-215
orthogonal, 39, 89, 234
permutation, 24
pivot, 21, 22, 53, 74, 75, 231
powers, 60, 227
projection, 38
pseudo inverse, 42, 47
rank, 25, 26, 38, 44, 75
resolvent, 195
row space, 25, 28, 44, 211-215
singular, 75
square, 51, 81
symmetric, 37, 38, 73-75, 81-84, 230
trace, 54
trapezoidal, 24
triangular, 21, 22, 41, 53, 54
tridiagonal, 88
unitary, 64
metric
du 138, 139, 152, 153, 271-274, 277
d 2 , 138, 141, 149, 152, 153, 271,
274-275, 277
doo, 138, 140, 152, 153, 271, 276-277

closed ball, 139, 152, 271

discrete, 137, 139, 141, 271

open, 149

open ball, 139, 143, 152, 271

space, 137, 157-166, 279

metricspaces, 137-154

multi-commodity network flow problem,

116, 257-264

multi-set problem, 209, 287, 288

multinomial theorem, 286

natural, 129

neighborhood, 94

Newton's method, 281

norm, 33-35, 40, 82-89, 137

h, 34, 138, 153, 272-274, 277

h, 34, 138, 153, 274-275, 277

loo, 34, 138, 153, 276-277

matrix, 84-86, 234-240

number systems, 121-134, 266-270

octahedron, 100, 241

orthogonality, 35-47

complement, 35

Gram-Schmidt, 40, 87

orthonormality, 39

vector space, 35

pivot, 21, 22, 53, 108, 110

point

basic, 105, 246, 250

bfs, 105, 246, 250

boundary, 71, 77, 94, 231

extreme, 93, 94, 98-100, 105, 115,

246, 250

interior, 94, 140

isolated, 142, 158, 165, 170

limit, 142, 143, 150, 158, 179

maximum, 71-73, 77, 233

minimum, 71-73, 76, 77, 233

neighborhood, 142, 143

saddle, 71, 73

stationary, 73, 77, 231

polyhedron, 96

polynomial, 18, 20, 29, 170, 212

characteristic, 51

derivative, 20, 29, 213

integral, 29, 214

minimal, 58