Index 313 flag, 188 Fn, 2 Fourier coefficients, 30 Fourier series, 29 Frobenius, 153, 252, 262 Frobenius norm, 77, 118, 123 Frobenius normal form, 242 Frobenius–Schur index, 245 full column rank, 70 general digraph, 235 general graph, 223 generalized Hamming code, 272 generator matrix, 268–269 geometric multiplicity, 40 Gerˇ sgorin Circle Theorem, 45–46, 119, 252 Givens, 149 Gram–Schmidt orthogonalization process, 33 graph, 169, 221 characteristic polynomial of, 226 complement of, 232 complete, 222 connected, 225 cubic, 223 diameter, 225 edge, 221 general, 223 imprimitive, 242 isomorphic, 222 order, 221 primitive, 242 regular, 223 simple, 222 spectrum, 226 strongly regular, 227–231 vertex, 221 Hadamard, 33 Hadamard codes, 276 Hadamard determinant inequality, 33, 37, 105 Hadamard matrices, 207–208 Hadamard product, 15, 178 Hall, Philip, 174–175 Hamming code, 266–267, 271–272 generalized, 272 Hamming distance, 269 Helly’s theorem, 181 Hermitian matrix, 8, 92, 139 eigenvalues, 94, 95, 97 field of values, 144 inertia, 92, 102 principal submatrix of, 97 repeated eigenvalue, 98 Hessenberg matrix, 131 Hilbert space, 25, 27 Hoffman, 154, 179 Hoffman–Wielandt theorem, 154, 178–180 homogeneous linear system, 285 Householder matrix, 38 Householder transformation, 38, 127–133 hyperplane, 23 identity matrix, 5 image, 4 imprimitive graph, 242 imprimitive matrix, 260–262 incidence matrices for 2-designs, 189–191 incidence matrix, 171 incident, 222 indefinite, 100 indegree, 235 index of imprimitivity, 242–244 index of nilpotency, 57 induced norm, 117 inertia Sylvester’s law, 93–94 inertia of a Hermitian matrix, 92, 102 initial vertex, 235 injective, 4 inner product, 17 conjugate bilinear, 17 conjugate symmetric, 17 in Cn, 21–22 standard, 18 symmetric, 17 interlacing theorem, 97 invariant subspace, 10, 151 inverse power method, 136 invertible, 4, 6 irreducible components, 242 irreducible matrix, 238, 259–260 isolated vertex, 222 isomorphic, 4 isomorphic graphs, 222 isomorphism, 4 J, 163 Jacobi identity, 157
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