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- Keyword
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- $(R (2)
- $R$-symmetric (2)
- Eigenvalue problem (2)
- $(\mathbf{R} (1)
- Approximation problem (1)
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- Approximation; Frobenius norm; involution; Moore–Penrose inverse (1)
- Asymptotic behavior (1)
- Centrosymmetric (1)
- Commute (1)
- Convergence (1)
- Difference equations (1)
- Frobenius norm (1)
- Hermitian (1)
- Infinite products of matrices (1)
- Inverse (1)
- Inverse eigenproblem; $R$-skew symmetric (1)
- Least Squares problem (1)
- Moore--Penrose Inverse (1)
- Moore--Penrose inverse (1)
- Moore–Penrose inverse (1)
- S)$-skew symmetric; $(R (1)
- S)$-symmetric (1)
- S_{\sigma})$-commutative (1)
- Singular value decomposition (1)
- \mu)$ symmetric (1)
Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench
Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench
William F. Trench
Let $R=P \diag(\gamma_{0}I_{m_{0}}, \gamma_{1}I_{m_{1}}, \dots, \gamma_{k-1}I_{m_{k-1}})P^{-1}\in\mathbb{C}^{m\times m}$ and $S_{\sigma}=Q\diag(\gamma_{\sigma(0)}I_{n_{0}},\gamma_{\sigma(1)}I_{n_{1}}, \dots,\gamma_{\sigma(k-1)}I_{n_{k-1}})Q^{-1}\in\mathbb{C}^{n\times n}$, where $m_{0}+m_{1}+\cdots +m_{k-1}=m$, $n_{0}+n_{1}+\cdots+n_{k-1}=n$, $\gamma_{0}$, $\gamma_{1}$, \dots, $\gamma_{k-1}$ are distinct complex numbers, and $\sigma :\mathbb{Z}_{k}\to\mathbb{Z}_{k}= \{0,1, \dots, k-1\}$. We say that $A\in\mathbb{C}^{m\times n}$ is $(R,S_{\sigma})$-commutative if $RA=AS_{\sigma}$. We characterize the class of $(R,S_{\sigma})$-commutative matrrices and extend results obtained previously for the case where $\gamma_{\ell}=e^{2\pi i\ell/k}$ and $\sigma(\ell)=\alpha\ell+\mu \pmod{k}$, $0 \le \ell \le k-1$, with $\alpha$, $\mu\in\mathbb{Z}_{k}$. Our results are independent of $\gamma_{0}$, $\gamma_{1}$, \dots, $\gamma_{k-1}$, so long as they are distinct; i.e., if $RA=AS_{\sigma}$ for some choice of $\gamma_{0}$, $\gamma_{1}$, \dots, $\gamma_{_{k-1}}$ (all distinct), then $RA=AS_{\sigma}$ for arbitrary of …
Multilevel Matrices With Involutory Symmetries And Skew Symmetries, William F. Trench
Multilevel Matrices With Involutory Symmetries And Skew Symmetries, William F. Trench
William F. Trench
No abstract provided.
Inverse Eigenproblems And Associated Approximation Problems For Matrices With Generalized Symmetry Or Skew Symmetry, William F. Trench
Inverse Eigenproblems And Associated Approximation Problems For Matrices With Generalized Symmetry Or Skew Symmetry, William F. Trench
William F. Trench
No abstract provided.
Minimization Problems For (R,S)-Symmetric And (R,S)-Skew Symmetric Matrices, William F. Trench
Minimization Problems For (R,S)-Symmetric And (R,S)-Skew Symmetric Matrices, William F. Trench
William F. Trench
No abstract provided.
Invertibly Convergent Infinite Products Of Matrices, With Applications To Difference Equations, William F. Trench
Invertibly Convergent Infinite Products Of Matrices, With Applications To Difference Equations, William F. Trench
William F. Trench
No abstract provided.