Wolkowicz, H. and Styan, G. P. (1980), `More bounds for elgenvalues using traces', Linear Algebra and its Applications 31(1), 1 - 17.Wolkowicz, H (1980) More bounds for eigenvalues using traces. Linear Algebra and Its Applications 31: pp. 1-17...
where ∂i= ∂ρ/∂ifor some density matrix parameterized by a vector\(\bar{\theta }=\{{\theta }_{1}\ldots {\theta }_{m}\}\), and we writei,jas shorthand for the parametersθi,θj.λi,λjrepresent the eigenvalues associated with ∂iρand ∂jρ. The quantum Fisher inf...
where ∂i= ∂ρ/∂ifor some density matrix parameterized by a vector\(\bar{\theta }=\{{\theta }_{1}\ldots {\theta }_{m}\}\), and we writei,jas shorthand for the parametersθi,θj.λi,λjrepresent the eigenvalues associated with ∂iρand ∂jρ. The quantum Fisher inf...
The points wi of HSkels(γ ) appear in order as one traces γ in the direction of positive orientation. We denote the polygonal path w0 → w1 →···→ wm+1 by HPaths(γ ). The specifics of the algorithm for choosing the s-hull skeleton are not important to us here; we refer ...
Yellow steps, for all spatial filters corresponding to individual cell bodies, we thresholded the filters at 5% of each filter’s maximum intensity and set to zero any filter components with non-zero weights outside the soma. To attain neural activity traces, we then reapplied the set of ...
However, this is not the case for scale-free and small-world networks and this makes their entropy analysis more challenging. In this paper, we try to overcome this problem using some existing inequalities on the largest eigenvalues of the graphs. Our key contributions are as follows. The ...
seems of little relevance to our problem. 2. Eigenvalues, entropy, and linear circuits. Let A be an n × n matrix with integer elements. A linear circuit for computing y = Ax, where x ∈ R n , is a directed acyclic graph with n input nodes x = (x 1 , . . . , x n ...
MATRIXSignlessLAPLACIANMATRIXBOUNDSofEIGENVALUEIn this paper, we found the bounds of the extreme eigenvalues of normalized Laplacian matrices and signless Laplacian matrices by using their traces. In addition, we found the bounds for k-th eigenvalues of normalized Laplacian matrix and signless ...
Our results here are fundamentally profound because of several reasons. Firstly, the tight bounds presented here are explicitly computable (e.g. in terms of the Kraus operators of a noisy channel), without any knowledge of the eigenvalues and the eigenvectors of the evolved probe state20,27and ...
Bounds for eigenvalues using trace[J].Linear Algebra and Its Applications,1980.471-506.Wolkowicz, H., Styan, G.: Bounds for eigenvalues using traces. Linear Algebra Appl. 29 , 471–506 (1980) MathSciNet MATHH. Wolkowicz and G.P.H. Styan. Bounds for eigenvalues using traces. Linear ...