Index absorbing Markov chain, 297 absorbing state, 297 additive commutator, 156 adjacency matrix, 223–225 adjacency matrix of a digraph, 236 adjacency matrix of a graph, 170 adjacent edges, 222 adjacent vertices, 169 adjoint, 18, 36 A F , 77 algebraic multiplicity, 41 asymptotically stable, 289 balanced incomplete block design, 185, 189–191 banded, 131 bandwidth, 131 basis, 3 Bessel’s inequality, 28, 31 best least squares fit, 26 BIBD, 185, 189–191 symmetric, 190–191 bidiagonal, 130 bijective, 4 bilinear form, 89 conjugate bilinear, 90 conjugate symmetric, 90 symmetric, 89 Birkhoff theorem, 176–178 block cycle matrices, 165–167 block cyclic form, 244 block cyclic matrices, 244 block design, 185, 189 symmetric, 190–191 block diagonal, 11 block triangular, 11 block triangular matrice, 84 block triangular matrix, 80 Bruck–Ryser–Chowla theorem, 187, 192, 202–204 C[a, b], 18 canonical form, 51 Cauchy’s interlacing theorem, 97 Cauchy–Schwarz inequality, 20 Cayley–Hamilton theorem, 64–65 chain, 224 directed, 236 change of basis, 6–7 change of basis matrix, 6 characteristic polynomial, 39 characteristic polynomial of a graph, 226 characteristic values, 40 Cholesky decomposition, 140 circulant matrices, 163–165 closed walk, 224 cofactors, 12 expansion by, 12 cohort model, 281 Collatz, 253 column operations, 102–105 column rank, 5 column space, 5 commutator, additive, 156 companion matrix, 66 311

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