Zobrazeno 1 - 10
of 191
pro vyhledávání: '"Götz Trenkler"'
Autor:
Oskar Maria Baksalary, Götz Trenkler
Publikováno v:
Examples and Counterexamples, Vol 6, Iss , Pp 100155- (2024)
The problem of establishing an upper bound for the volume of a parallelepiped is considered by utilizing an original approach involving a skew-symmetric matrix of order four (along with its Moore–Penrose inverse). It is shown that the commonly know
Externí odkaz:
https://doaj.org/article/2e58ee4965084dcf8b642b2a71c9b20c
Autor:
Oskar Maria Baksalary, Götz Trenkler
Publikováno v:
Examples and Counterexamples, Vol 4, Iss , Pp 100118- (2023)
The paper considers diagonalization of the cross-product matrices, i.e., skew-symmetric matrices of order three. A procedure to determine a nonsingular matrix, which yields the diagonalization is indicated. Furthermore, a method to derive the inverse
Externí odkaz:
https://doaj.org/article/c90f334865974d4a8bd7e9cb58500c99
Publikováno v:
Croatian Operational Research Review, Vol 2, Iss 1, Pp 4-13 (2011)
We study singular magic matrices in which the numbers in the rows and columns and in the two main diagonals all add up to the same sum. Our interest focuses on such magic matrices for which the Moore–Penrose inverse is also magic. Special attention
Externí odkaz:
https://doaj.org/article/89cb774c27cf492588082ba3aec07874
Autor:
Oskar Maria Baksalary, Götz Trenkler
Publikováno v:
Statistical Papers. 63:1499-1509
An alternative look at the linear regression model is taken by proposing an original treatment of a full column rank model (design) matrix. In such a situation, the Moore–Penrose inverse of the matrix can be obtained by utilizing a particular formu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1e7d4c3694db938b19bff8a2aa14b259
https://doi.org/10.1007/s00362-021-01280-x
https://doi.org/10.1007/s00362-021-01280-x
Autor:
Götz Trenkler, Oskar Maria Baksalary
Publikováno v:
Indian Journal of Pure and Applied Mathematics. 52:323-334
It is known that within the set of orthogonal projectors (Hermitian idempotent matrices) certain matrix partial orderings coincide in the sense that when two orthogonal projectors are ordered with respect to one of the orderings, then they are also o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2b6331eeff331b339ffe1c321d2681ec
https://doi.org/10.1007/s13226-021-00138-0
https://doi.org/10.1007/s13226-021-00138-0
Autor:
Götz Trenkler, Oskar Maria Baksalary
Publikováno v:
Linear and Multilinear Algebra. 70:2014-2026
The paper investigates the class of square matrices which have idempotent Moore–Penrose inverse. A number of original characteristics of the class are derived and new properties identified. Additio...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e807ae6db2f73f6cb0d9513a9e71ad0b
https://doi.org/10.1080/03081087.2020.1781038
https://doi.org/10.1080/03081087.2020.1781038
Autor:
Götz Trenkler, Heinz Neudecker
Publikováno v:
Discussiones Mathematicae Probability and Statistics. 25:207
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f5b7d21993c6204eaa93d43e98352d4c
https://doi.org/10.7151/dmps.1069
https://doi.org/10.7151/dmps.1069
Autor:
Oskar Maria Baksalary, Götz Trenkler
Publikováno v:
The European Physical Journal H. 46
The Moore–Penrose inverse celebrated its 100th birthday in 2020, as the notion standing behind the term was first defined by Eliakim Hastings Moore in 1920 (Bull Am Math Soc 26:394–395, 1920). Its rediscovery by Sir Roger Penrose in 1955 (Proc Ca
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::85dab22ebbfc77aea495a7c60d72b4c6
https://doi.org/10.1140/epjh/s13129-021-00011-y
https://doi.org/10.1140/epjh/s13129-021-00011-y
Publikováno v:
Linear and Multilinear Algebra. 68:1411-1423
A simple parametrization for 4 × 4 most perfect magic (MPM) squares is derived. This parametrization permits to calculate their powers and eigenvalues as well as their Moore–Penrose, group, and cor...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::023816299a1f10744d8f7889d0a9f165
https://doi.org/10.1080/03081087.2018.1545005
https://doi.org/10.1080/03081087.2018.1545005
Autor:
Oskar Maria Baksalary, Götz Trenkler
Publikováno v:
Applied Mathematics and Computation. 403:125913
The paper revisits the considerations carried out in [J.K. Baksalary, O.M. Baksalary, Linear Algebra Appl. 421 (2007) 16–23], where particular formulae for the Moore–Penrose inverse of a columnwise partitioned matrix were derived. An impuls to re
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::cfedcd93867b214101acd1d0487c5f19
https://doi.org/10.1016/j.amc.2020.125913
https://doi.org/10.1016/j.amc.2020.125913