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- Published Research Papers (5)
- $(R (2)
- $R$-symmetric (2)
- Eigenvalue problem (2)
- $(\mathbf{R} (1)
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- Approximation problem (1)
- 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})$-commutative (1)
- Singular value decomposition (1)
- Statistical Models (1)
- \mu)$ symmetric (1)
- Publication
Articles 1 - 7 of 7
Full-Text Articles in Analysis
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 …
The 1905 Einstein Equation In A General Mathematical Analysis Model Of Quasars, Byron E. Bell
The 1905 Einstein Equation In A General Mathematical Analysis Model Of Quasars, Byron E. Bell
Byron E. Bell
No abstract provided.
A Mathematical Regression Of The U.S. Gross Private Domestic Investment 1959-2001, Byron E. Bell
A Mathematical Regression Of The U.S. Gross Private Domestic Investment 1959-2001, Byron E. Bell
Byron E. Bell
SUMMARY OF PROJECT What did I do? A study of the role the U.S. stock markets and money markets have possibly played in the Gross Private Domestic Investment (GPDI) of the United States from the year 1959 to the year 2001 and I created a Multiple Linear Regression Model (MLRM).
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.