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A canonical form is a labeled graph Canon(G) that is isomorphic to G, such that every graph that is isomorphic to G has the same canonical form as G. Thus, from a solution to the graph canonization problem, one could also solve the problem of graph isomorphism : to test whether two graphs G and H are isomorphic, compute their canonical forms ...
A canonical form is a labeled graph Canon(G) that is isomorphic to G, such that every graph that is isomorphic to G has the same canonical form as G. Thus, from a solution to the graph canonization problem, one could also solve the problem of graph isomorphism : to test whether two graphs G and H are isomorphic, compute their canonical forms ...
Canonical forms may also be called canonical invariants or complete invariants, and are sometimes defined only for the graphs within a particular family of graphs. Graph canonization is the process of computing a canonical form. card A graph formed from a given graph by deleting one vertex, especially in the context of the reconstruction ...
The Jordan form is used to find a normal form of matrices up to conjugacy such that normal matrices make up an algebraic variety of a low fixed degree in the ambient matrix space. Sets of representatives of matrix conjugacy classes for Jordan normal form or rational canonical forms in general do not constitute linear or affine subspaces in the ...
The main problem of quantum many-body physics is the fact that the Hilbert space grows exponentially with size. In other words if one considers a lattice, with some Hilbert space of dimension on each site of the lattice, then the total Hilbert space would have dimension , where is the number of sites on the lattice.
The transfer function coefficients can also be used to construct another type of canonical form ˙ = [] + [] () = [] (). This state-space realization is called observable canonical form because the resulting model is guaranteed to be observable (i.e., because the output exits from a chain of integrators, every state has an effect on the output).
Here, E is a function from the space of states to the real numbers; in physics applications, E(x) is interpreted as the energy of the configuration x. The parameter β is a free parameter; in physics, it is the inverse temperature. The normalizing constant Z(β) is the partition function. However, in infinite systems, the total energy is no ...
Every vector a in three dimensions is a linear combination of the standard basis vectors i, j and k.. In mathematics, the standard basis (also called natural basis or canonical basis) of a coordinate vector space (such as or ) is the set of vectors, each of whose components are all zero, except one that equals 1. [1]