314 Index Jn, 40 Jordan block, 58 Jordan canonical form, 52, 63–64 Jp(λ), 58 kernel, 3 Km,m, 227 K¨ onig–Egerv´ ary theorem, 173 Kronecker delta, 35 l2, 116 L property, 158–161 Lagrange expansion by cofactors, 12 Lagrange four-square theorem, 202 latent roots, 40 lattice graph L2(m), 231 LDU factorization, 138–140 least squares fit, 26 left eigenvector, 40 length of a vector, 17, 18 Leslie matrix, 282 Lie algebra, 157 line, 3 line of a matrix, 173 linear code, 267–269 linear combination, 2 linear constant coeﬃcient systems, 285–288 linear dynamical system, 279–281 linear functional, 35 linear transformation, 3 linearly dependent, 2 linearly independent, 2 loop, 169, 221, 222, 235 lower triangular matrix, 9 lp-norm, 114 l2, 25 L2(a, b), 30 majorization, 180 Markov chain, 295–300 absorbing, 297 Markov process, 295–300 matrix, 4 block diagonal, 11 block triangular, 11, 80 companion, 66 diagonal, 8 equivalent, 7 Hermitian, 8, 92, 139 imprimitive, 260–262 irreducible, 259–260 lower triangular, 9 m × n, 4 nilpotent, 57–61 nonderogatory, 66 nonnegative, 249, 258–259 normal, 78, 81–83 of a linear transformation, 5 orthogonal, 32 positive, 249 positive definite, 22, 99–102 primitive, 260–262 product, 4 similar, 7, 40 skew-Hermitian, 8 skew-symmetric, 8 strictly lower triangular, 9 strictly upper triangular, 9 symmetric, 8, 139 tensor product of, 13 triangular, 9, 40 unitary, 15, 32 upper triangular, 9 matrix norms, 117–118 max norm, 114 maximin, 95–96 McCoy’s theorem, 157–158 Metzler matrix, 293 minimal polynomial, 65–66 minimax, 95–96 minimum distance of a code, 270–271 Minkowski’s inequality, 114 multigraph, 223 multiple edges, 223 multiplicity algebraic, 41 geometric, 40 nearest neighbor decoding, 269–270 negative definite, 99, 101 negative semi-definite, 99 nil algebra, 156 nil ideal, 156 nilpotent algebra, 156 nilpotent ideal, 156 nilpotent matrix, 57–61 nonderogatory, 66 nonnegative matrix, 249, 258–259 nonnegative system, 292 nonsingular, 6 norm, 113–118, 123 norm, Frobenius, 77 normal matrix, 78, 81–83

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