Maclaurin series, 606

Manchester (England), 330

Mass matrix, 425, 446

Mass-spring system, 266, 302, 309, 366, 425, 427, 432, 496, 507, 539, 570, 571, 580, 596

Mathematical model, modeling, 4

Matrix, 147

• addition, 164

• adjoint, 199, 675

• augmented, 148

• coefficient, 147

• cofactor, 190, 675

• column, 147

• determinant, 188

• diagonal, 174

• diagonalizable, 349, 352

• echelon, 150

• eigenvalue, 330, 386

• eigenvector, 339, 386

• element, 147

• elementary, 180

• elementary row operations, 149

• entry, 147

• equality, 164

• exponential, 472

• fundamental, 469

• identity, 162, 172, 175

• inverse, 177, 676

• invertible, 177

• Jacobian, 516

• minor, 190

• multiplication by scalar, 165

• negative of, 165

• nilpotent, 474

• nonsingular, 183

• norm, 658

• orthogonal, 202

• principal diagonal, 162

• product, 168

• projection matrices of, 491

• reduced echelon, 157

• row, 147

• shape, 147

• similar, 349

• singular, 183

• size, 147

• spectral decomposition, 493

• square, 161

• stochastic, 357

• trace, 347

• transition, 356

• triangular, 194

• transpose, 195

• with distinct eigenvalues, 352

• zero, 172

Matrix algebra, 171

Matrix differential equation, 376, 469

Matrix equations, 182

Matrix exponential, 494, 499

Matrix exponential solution, 475

Matrix-valued function, 375

• continuous, 375

• differentiable, 375

• derivative of, 375

Mechanical systems (modeling), 331

Method of elimination, 140

• for determinants, 194

Method of Frobenius, 631

Method of successive approximations, 654

Method of undetermined coefficients, 314, 316, 320

• for nonhomogeneous systems, 483

Mexico City, 330

Minimal spanning set, 242

Minor (of a matrix), 190

Mixture problems, 51

Mks units, 13

Modulus (of complex number), 298

Multiplication by an elementary matrix, 671

Multiplication of matrices, 168

• and determinants, 196

• associative law, 171

• by scalars, 165

Multiplication of vector by scalar, 213

Multiplicity of eigenvalue, 354, 437

Multistory building, 435

Mutual extinction, 359