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pro vyhledávání: '"Ralph John de la Cruz"'
Autor:
Ralph John de la Cruz
Publikováno v:
Science Diliman, Vol 27, Iss 2, Pp 1-9 (2015)
Let F be a f ield. It is a classical result in linear algebra that for each A, P ϵ Mn (F) such that P is nonsingular, tr A = tr (PAP-1). We show in this paper that the preceding property does not hold true if F is the division ring of real quaternio
Externí odkaz:
https://doaj.org/article/a21cf325af714189a1732d3ce49a6a28
Autor:
Ralph John De la Cruz, Agnes T. Paras
Publikováno v:
The Electronic Journal of Linear Algebra. :655-660
An $n$-by-$n$ matrix $A$ is called symmetric, skew-symmetric, and orthogonal if $A^T=A$, $A^T=-A$, and $A^T=A^{-1}$, respectively. We give necessary and sufficient conditions on a complex matrix $A$ so that it is a sum of type ``"orthogonal $+$ symme
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::56ecf4dc44c8f5f6011ad87697db3d1e
https://doi.org/10.13001/ela.2022.7129
https://doi.org/10.13001/ela.2022.7129
Publikováno v:
The Electronic Journal of Linear Algebra. :463-482
A square matrix $A$ is an involution if $A^{2} = I$. The centralizer of a square matrix $S$ denoted by $\mathscr{C}(S)$ is the set of all $A$ such that $AS = SA$ over an algebraically closed field of characteristic not equal to 2. We determine necess
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a4796db40419159f8752da63b47401d6
https://doi.org/10.13001/ela.2022.7091
https://doi.org/10.13001/ela.2022.7091
Publikováno v:
Linear Algebra and its Applications. 620:201-227
Let B = J 2 n or B = R n for the matrices given by J 2 n = [ I n − I n ] ∈ M 2 n ( C ) or R n = [ 1 ⋰ 1 ] ∈ M n ( C ) . A matrix A is called B-normal if A A ⋆ = A ⋆ A holds for A and its adjoint matrix A ⋆ : = B − 1 A H B . In additio
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fd2ad665d6bd623805a107b8f56fa30b
https://doi.org/10.1016/j.laa.2021.03.003
https://doi.org/10.1016/j.laa.2021.03.003
Publikováno v:
The Electronic Journal of Linear Algebra. 37:387-401
For an indefinite scalar product $[x,y]_B = x^HBy$ for $B= \pm B^H \in \mathbf{Gl}_n(\mathbb{C})$ on $\mathbb{C}^n \times \mathbb{C}^n$, it is shown that the set of diagonalizable matrices is dense in the set of all $B$-normal matrices. The analogous
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::47a1da43de53940d52ec7973a1a5f08f
https://doi.org/10.13001/ela.2021.5509
https://doi.org/10.13001/ela.2021.5509
Autor:
Ralph John de la Cruz
Publikováno v:
Operators and Matrices. :677-684
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8d44b605f3b9a153172c4e8ed06a45ff
https://doi.org/10.7153/oam-2021-15-45
https://doi.org/10.7153/oam-2021-15-45
Autor:
Ralph John de la Cruz, Edgar N. Reyes
Publikováno v:
Communications in Algebra. 49:932-947
Let M be the backward identity matrix. A complex matrix G is perplectic if G is an isometry of the symmetric scalar product ( x , y ) → x T M y , that is, ( x , y ) = ( G x , G y ) for all column v...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d4c4a7bb105c15cd13ba887a933eb8f5
https://doi.org/10.1080/00927872.2020.1823403
https://doi.org/10.1080/00927872.2020.1823403
Autor:
Ralph John de la Cruz, Agnes T. Paras
Publikováno v:
Linear Algebra and its Applications. 603:84-90
A complex 2 n × 2 n matrix A is called skew-Hamiltonian, Hamiltonian, and symplectic if A J = A , A J = − A , and A J = A − 1 , respectively, in which J = [ 0 I n − I n 0 ] and A J = J − 1 A T J . We prove that each 2 n × 2 n matrix is a su
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ea80817c2ee994553fda387cd56e8f40
https://doi.org/10.1016/j.laa.2020.05.036
https://doi.org/10.1016/j.laa.2020.05.036
Publikováno v:
Linear Algebra and its Applications. 591:61-71
Let R n be the n-by-n backward identity matrix and let L n , k : = I k ⊕ − I n − k . Suppose A ∈ C n × n is nonsingular. We say that A is perplectic if R n A T R n = A − 1 ; and A is pseudo-unitary if L n , k A ⁎ L n , k = A − 1 . We g
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::599e732e798443631a1d3afca62b91c0
https://doi.org/10.1016/j.laa.2020.01.010
https://doi.org/10.1016/j.laa.2020.01.010
Autor:
Ralph John de la Cruz, Dominic Awa
Publikováno v:
Linear Algebra and its Applications. 589:85-95
A 2n-by-2n matrix A is symplectic if A T [ 0 I − I 0 ] A = [ 0 I − I 0 ] . It is known that if n > 1 , then every 2n-by-2n complex symplectic matrix is a product of four symplectic involutions. We consider the real case. We give an example of a r
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3b8996a999e41e471a842be08989c282
https://doi.org/10.1016/j.laa.2019.12.003
https://doi.org/10.1016/j.laa.2019.12.003