(4):1735–1756, 2009). The new matrix rank-one decomposition theorems appear to have wide applications in theory as well as in practice. On the theoretical side, for example, we show how to further extend some of the classical results including a lemma due to Yuan (Math Program 47:53–...
内容提示: arXiv:1811.05854v2 [math.NA] 16 Nov 2018When is a matrix unitary or Hermitian plus low rank? ∗Gianna M. Del Corso, Federico Poloni, Leonardo Robol, andRaf Vandebril †November 28, 2018AbstractHermitian and unitary matrices are two representatives of the class of normal matrices...
Instead, the number of an eigenvalue [Math Processing Error]λ of the nonlinear problem (1) is inherited from the number of the eigenvalue 0 of the matrix [Math Processing Error]T(λ) based on the following consideration:Definition 3
$$\begin{aligned} R^{\text {GinOE}}_{N}(\varvec{z})&= \frac{1}{\pi ^{k(2k-1)}} \int _{{\mathcal {A}}_{2k}({\mathbb {C}})} dX e^{- \frac{1}{2}{{\,\textrm{Tr}\,}}XX^\dag }\, \text {Pf} \left( {\begin{matrix} X & & Z\\ -Z & & X^{\dagger ...
Notice that the unit matrix 𝐶00−𝜎0C00−σ0 is a trivial operation that can be removed in practice. The other two jointly controlled gates are necessary, and their matrix forms are 𝐶01−𝑉1=⎡⎣⎢⎢⎢⎢𝜎00000𝑉10000𝜎00000𝜎0⎤⎦⎥⎥⎥⎥C01−V...
Using our present notation conventions we may summarize that the predictions mediated by the SP and NSP calculations are indistinguishable, in essence, due to the coincidence of matrix elements ≺𝜓(𝑡)|𝔮|𝜓(𝑡)≻=〈〈𝜓(𝑡)|𝑄|𝜓(𝑡)〉.≺ψ(t)|q|ψ(t)≻=...