Sentence examples for unitary basis from inspiring English sources

It is independent of the choice of unitary basis and defines a linear functional on the space (C_1) of operators of trace class.

If L is of trace class, then for every unitary basis ({ u_i }) of (mathcal {V}) the trace begin{aligned} mathrm {Tr},L := sum langle u_i,, L, u _irangle end{aligned}converges absolutely.

Consider the signal f=[σ1,…,σ N ] T with N=N x N y that can be sparsely represented by means of the transform matrix Ψ, which describes an N×N unitary basis such that f = Ψ H χ, (23).

People advising the Greenspan Commission believed in the lock box: "Some have argued that Social Security's investment income should be ignored because it involves inter-fund transfers which are not shown when the federal budget is displayed on a unitary basis and are irrelevant for the limited exercise of macroeconomic analysis".

These activities will be valued on a unitary basis.

Next we calculated the FI per neuron for a large family of cubic lattices L φ, ψ generated by three unitary basis vectors with spanning angles φ and ψ. Figure 4D displays tr J L φ, ψ for θ1 = θ2 = 1/4 and various φ and ψ.

Chang argues that her covering values are sufficiently unitary to provide a basis for comparison, and yet preserve the separateness of the other values.

The question of how we represent numbers and whether there is a unitary cognitive and neuronal basis for all forms of numerical representation is therefore an important problem.

For example, the motivation for two recent fMRI studies was, in part, to find the neural basis of a "unitary dominant eye" [ 2, 6].

Looked at as a whole, there is no doubt that the Convention represents an opportunity, yet Parliament contradicts Laeken by demanding that we should negotiate and reach a decision on the basis of one unitary, coherent proposal.

Although the commission recommended that Leeds should form the basis of a new unitary "one tier county" no action was taken.