The main idea is to reduce the problem to determinants of other operators whose determinant asymptotics are well known.
The new algorithm produces a smaller matrix whose determinant is a nontrivial multiple of the Sparse Resultant and from which the latter is easily recovered.
It should be also noted that particular attention is given to reduce the size of the system matrix whose determinant equation yields eigenvalues, and to overcome the functional dependence problem of the non-dimensional dynamic influence functions.
We show that the fixed point algebra OG of the Cuntz algebra On n = 2, 3...,∞, under the canonical action of a strongly compact group G of unitaries on the generating Hubert space H is simple if the defining representation of G is a direct sum of finite dimensional representations whose determinant takes values in finite subgroups of the circle.
These are the members of GL ( n ) whose determinant is one.
whose determinant does not vanish for any x ∈ [ 0, T ] by virtue of Theorem 5.
The group of special affine transformations is denoted by, these are the members of whose determinant is one.
Equalities (24) are a k-dimensional linear system in variables (c_{s}), (s=overline {0,k-1}), whose determinant is (V_{k}(1,varepsilon,ldots, varepsilon ^{k-1})=:V_{k}).
The matrix of the linear system (4), t i, ε j, is a Vandermonde matrix whose determinant has a positive lower bound, because ti,ϵ- ti',ϵ≥ 1/N + 1 for i > i'.
Furthermore if we ensure that each A k is also a P-matrix, i.e. a matrix whose determinant and all principal minors are positive[24], we can deduce that its inverse is well defined.
