Appendices
Jerome R. Busemeyer, Peter Bruza · 2012
Notation Below is a brief list of the notation used in this book. In general, the Dirac notation is used for abstract vectors and operators that are expressed in a coordinate free manner, and traditional matrix algebra notation is used when a vector or an operator is expressed in terms of coordinates of a specific basis. N is the dimension of a Hilbert space a, b, c, x, y, z are scalars which can be complex numbers X, Y, P, Q are matrices diag[ X ] is a diagonal matrix formed from the N × 1 column matrix X α, β, γ are often used to represent N × 1 column matrices of amplitudes α i is one coordinate value of α; that is, a single amplitude X † is the Hermitian transpose of X X −1 is the inverse of the full rank matrix X If α is an N × 1 column matrix, then α † is an 1 × N row matrix of conjugate values (α † · β) is the inner product of two N × 1 column matrices (α, β) ψ · φ † is the outer product matrix of two N × 1 column matrices (ψ, φ) Tr[ X ] is the trace of the square matrix X X ⊗ Y is the Kronecker product of two matrices V = {| V i ⟩, i = 1, N } orthonormal basis, or W = {| W i ⟩, i = 1, N } for another one | X ⟩ is an abstract vector; it can be represented by a N × 1 matrix α once you choose a basis