312 Index complement of a graph, 232 complete bipartite graph, 227 complete graph, 222 complete metric space, 27 complete orthonormal sequence, 28 components, strong, 236 condensation digraph, 240 configuration, 171 conformally partitioned, 10 congruence, 198 congruent matrices, 91 conjugate bilinear, 17 conjugate bilinear form, 90 conjugate symmetric bilinear form, 90 conjugate symmetric inner product, 17 conjugate transpose, 8 conjunctive matrices, 91 connected graph, 225 diameter, 225 continuous linear dynamical system, 279 convergence in the norm, 31, 114, 116 coordinates, with respect to a basis, 3 coset leader, 273 Courant–Fischer theorem, 95–96 covers, 274 cubic graph, 223, 227 cycle directed, 236 cycle in a graph, 224 deflation, 136 degree of a regular graph, 223 degree of a vertex, 222 determinant, 11–12, 175 diagonable, 42 diagonal matrix, 8 diagonalizability, 41–44 diagonalizable, 42 diagonalization, 41–44 diagonally dominant, 46 diameter of a graph, 225 difference equation, 280 differential equation, 280 digraph, 235 of a matrix, 237 dimension, 3 direct sum matrix, 11 subspace, 2 directed chain, 236 cycle, 236 trail, 236 directed edge, 235 directed graph, 235–238 directed walk, 236 discrete linear dynamical system, 279 distance between vertices of a graph, 225 dominant eigenvalue, 135 dot product, 4 doubly stochastic matrices, 176–178 dual basis, 35 dual space, 35 dynamical system, 279–281 Eckart–Young theorem, 124 edge directed, 235 edge of a graph, 169, 221 edges adjacent, 222 multiple, 223 eigenspace, 40 eigenvalue, 39–40 of a Hermitian matrix, 94, 95, 97 of a positive definite matrix, 100 eigenvector, 39 left, 40 elementary matrix, 112 elementary row and column operations, 102–105 elementary row operations, 138 ellipse, 145 endpoints of an edge, 222 entry-wise product, 178 equilibrium point, 289, 291 equivalent matrices, 7 equivalent norms, 114 error vector, 267, 269 error-correcting codes, 265–267 expansion by cofactors, 12 exponential of a matrix, 51 Fibonacci numbers, 279, 286 field, 1 field of values, 143–150 convexity, 148 two-by-two matrices, 145–147 finite dimensional, 3 finite projective planes, 191–197 first-order difference equation, 283 first-order differential equation, 283 fixed point, 289, 291
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