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To apportion a complex matrix means to apply a similarity so that all entries of the resulting matrix have the same magnitude. We initiate the study of apportionment, both by unitary matrix similarity and general matrix similarity. There are connecti
Externí odkaz:
http://arxiv.org/abs/2308.11808
Autor:
Xu, Chengshen
Markov matrices have an important role in the filed of stochastic processes. In this paper, we will show and prove a series of conclusions on Markov matrices and transformations rather than pay attention to stochastic processes although these conclus
Externí odkaz:
http://arxiv.org/abs/2003.13215
Autor:
Narayanan, H., Narayanan, Hariharan
One of the fundamental open problems in control theory is that of the stabilization of a linear time invariant dynamical system through static output feedback. We are given a linear dynamical system defined through \begin{align*} \mydot{w} &= Aw + Bu
Externí odkaz:
http://arxiv.org/abs/1810.11609
Autor:
Narayanan, H.
Linear systems often involve, as a basic building block, solutions of equations of the form \begin{align*} A_Sx_S&+A_Px_P =0\\ A'_Sx_S & =0, \end{align*} where our primary interest might be in the vector variable $x_P.$ Usually, neither $x_S$ nor $x_
Externí odkaz:
http://arxiv.org/abs/1609.07991
Let $A\in \mathbb{R}^{N\times N}$ and $\mathrm{SO}_n:=\{ U \in \mathbb{R}^{N \times N}:UU^t=I_n,\det U>0\}$ be the set of $n\times n$ special orthogonal matrices. Define the (real) special orthogonal orbit of $A$ by \[ O(A):=\{UAV:U,V\in\mathrm{SO}_n
Externí odkaz:
http://arxiv.org/abs/1608.06101
Maps $\Phi$ which do not increase the spectrum on complex matrices in a sense that $\Sp(\Phi(A)-\Phi(B))\subseteq\Sp(A-B)$ are classified.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
http://arxiv.org/abs/1210.0958
Autor:
Hariharan Narayanan, H. Narayanan
One of the fundamental open problems in control theory is that of the stabilization of a linear time invariant dynamical system through static output feedback. We are given a linear dynamical system defined through \begin{align*} \mydot{w} &= Aw + Bu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f048c80c87c596e45ab338d53616fbe1
Let A ∈ R n × n and SO n : = { U ∈ R n × n : U U t = I n , det U > 0 } be the set of n × n special orthogonal matrices. Define the (real) special orthogonal orbit of A by O ( A ) : = { U A V : U , V ∈ SO n } . In this paper, we show that the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1397f94616fc3ceb3204b619736baed1