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The state space or phase space is the geometric space in which the axes are the state variables. The system state can be represented as a vector , the state vector . If the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form.
By Gelfand representation, every commutative C*-algebra A is of the form C 0 (X) for some locally compact Hausdorff X. In this case, S(A) consists of positive Radon measures on X, and the pure states are the evaluation functionals on X. More generally, the GNS construction shows that every state is, after choosing a suitable representation, a ...
In quantum mechanics and computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system , named after the physicist Felix Bloch. [ 1 ] Mathematically each quantum mechanical system is associated with a separable complex Hilbert space H {\displaystyle H} .
State-space representation is especially powerful as it allows complex multi-order differential system to be solved as a system of first-order equations instead. The general form of the state equation is ˙ = + where () is a column matrix of the state variables, or the unknowns of the system.
A state-space model is a representation of a system in which the effect of all "prior" input values is contained by a state vector. In the case of an m-d system, each dimension has a state vector that contains the effect of prior inputs relative to that dimension. The collection of all such dimensional state vectors at a point constitutes the ...
The state of an isolated physical system is represented, at a fixed time , by a state vector | belonging to a Hilbert space called the state space. Separability is a mathematically convenient hypothesis, with the physical interpretation that the state is uniquely determined by countably many observations.
The configuration space of all unordered pairs of points on the circle is the Möbius strip. In mathematics, a configuration space is a construction closely related to state spaces or phase spaces in physics. In physics, these are used to describe the state of a whole system as a single point in a high-dimensional space.
The state-transition matrix is used to find the solution to a general state-space representation of a linear system in the following form ˙ = () + (), =, where () are the states of the system, () is the input signal, () and () are matrix functions, and is the initial condition at .