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pro vyhledávání: '"Woerdeman, Hugo J."'
We show that for a multivariable polynomial $p(z)=p(z_1, \ldots , z_d)$ with a determinantal representation $$ p(z) = p(0) \det (I_n- K (\oplus_{j=1}^d z_j I_{n_j}))$$ the matrix $K$ is structurally similar to a strictly $J$-contractive matrix for so
Externí odkaz:
http://arxiv.org/abs/2411.05385
Autor:
Gift, Sarah, Woerdeman, Hugo J.
Suppose $Q(x)$ is a real $n\times n$ regular symmetric positive semidefinite matrix polynomial. Then it can be factored as $$Q(x) = G(x)^TG(x),$$ where $G(x)$ is a real $n\times n$ matrix polynomial with degree half that of $Q(x)$ if and only if $\de
Externí odkaz:
http://arxiv.org/abs/2301.13776
Publikováno v:
In Linear Algebra and Its Applications 15 May 2024 689:247-259
Autor:
Poon, Edward, Woerdeman, Hugo J.
Publikováno v:
Linear Algebra and its Applications, Volume 631, 15 December 2021, Pages 174-180
We characterize under what conditions $n\times n$ Hermitian matrices $A_1$ and $A_2$ have the property that the spectrum of $\cos t A_1 + \sin t A_2$ is independent of $t$ (thus, the trigonometric pencil $\cos t A_1 + \sin t A_2$ is isospectral). One
Externí odkaz:
http://arxiv.org/abs/2103.12885
The multivariable autoregressive filter problem asks for a polynomial $p(z)=p(z_1, \ldots , z_d)$ without roots in the closed $d$-disk based on prescribed Fourier coefficients of its spectral density function $1/|p(z)|^2$. The conditions derived in t
Externí odkaz:
http://arxiv.org/abs/2101.00525
The relationship between a stable multivariable polynomial $p(z)$ and the Fourier coefficients of its spectral density function $1/|p(z)|^2$, is further investigated. In this paper we focus on the radial asymptotics of the Fourier coefficients for a
Externí odkaz:
http://arxiv.org/abs/2012.12980
Autor:
Gift, Sarah, Woerdeman, Hugo J.
Publikováno v:
In Linear Algebra and Its Applications 15 February 2024 683:125-150
Let $\mu_1$ be a complex number in the numerical range $W(A)$ of a normal matrix $A$. In the case when no eigenvalues of $A$ lie in the interior of $W(A)$, we identify the smallest convex region containing all possible complex numbers $\mu_2$ for whi
Externí odkaz:
http://arxiv.org/abs/2004.05288