Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Why use quantum theory for cognition and decision? Some compelling reasons
- 2 What is quantum theory? An elementary introduction
- 3 What can quantum theory predict? Predicting question order effects on attitudes
- 4 How to apply quantum theory? Accounting for human probability judgment errors
- 5 Quantum-inspired models of concept combinations
- 6 An application of quantum theory to conjoint memory recognition
- 7 Quantum-like models of human semantic space
- 8 What about quantum dynamics? More advanced principles
- 9 What is the quantum advantage? Applications to decision making
- 10 How to model human information processing using quantum information theory
- 11 Can quantum systems learn? Quantum updating
- 12 What are the future prospects for quantum cognition and decision?
- Appendices
- References
- Index
Appendices
Published online by Cambridge University Press: 05 August 2012
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Why use quantum theory for cognition and decision? Some compelling reasons
- 2 What is quantum theory? An elementary introduction
- 3 What can quantum theory predict? Predicting question order effects on attitudes
- 4 How to apply quantum theory? Accounting for human probability judgment errors
- 5 Quantum-inspired models of concept combinations
- 6 An application of quantum theory to conjoint memory recognition
- 7 Quantum-like models of human semantic space
- 8 What about quantum dynamics? More advanced principles
- 9 What is the quantum advantage? Applications to decision making
- 10 How to model human information processing using quantum information theory
- 11 Can quantum systems learn? Quantum updating
- 12 What are the future prospects for quantum cognition and decision?
- Appendices
- References
- Index
Summary
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
αi 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 = {|Vi⟩, i = 1, N} orthonormal basis, or W = {|Wi⟩, 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
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- Information
- Quantum Models of Cognition and Decision , pp. 361 - 384Publisher: Cambridge University PressPrint publication year: 2012