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Vector logic [1] [2] is an algebraic model of elementary logic based on matrix algebra. Vector logic assumes that the truth values map on vectors , and that the monadic and dyadic operations are executed by matrix operators.
Modern philosophers reject quantum logic as a basis for reasoning, because it lacks a material conditional; a common alternative is the system of linear logic, of which quantum logic is a fragment. Mathematically, quantum logic is formulated by weakening the distributive law for a Boolean algebra, resulting in an orthocomplemented lattice .
Quantity (common name/s) (Common) symbol/s Defining equation SI unit Dimension Wavefunction: ψ, Ψ : To solve from the Schrödinger equation: varies with situation and number of particles
As such, quantum states form a ray in projective Hilbert space, not a vector. Many textbooks fail to make this distinction, which could be partly a result of the fact that the Schrödinger equation itself involves Hilbert-space "vectors", with the result that the imprecise use of "state vector" rather than ray is very difficult to avoid. [5]
Due to linearity, vectors can be defined in any number of dimensions, as each component of the vector acts on the function separately. One mathematical example is the del operator, which is itself a vector (useful in momentum-related quantum operators, in the table below). An operator in n-dimensional space can be written:
Barwise compactness theorem (mathematical logic) Base change theorems (algebraic geometry) Basel problem (mathematical analysis) Bass-Guirvarc'h formula (group theory) Bass-Serre theorem (group theory) Basu's theorem ; Bauer–Fike theorem (spectral theory) Bayes' theorem (probability) Beatty's theorem (Diophantine approximation)
Common quantum logic gates by name (including abbreviation), circuit form(s) and the corresponding unitary matrices. In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of qubits.
The source free equations can be written by the action of the exterior derivative on this 2-form. But for the equations with source terms (Gauss's law and the Ampère-Maxwell equation), the Hodge dual of this 2-form is needed. The Hodge star operator takes a p-form to a (n − p)-form, where n is the number of dimensions.