A note to my paper “Generalized equivalence of collections of matrices and common divisors of matrices”
We correct some misprints and other oversights in the paper mentioned in the title.
Збережено в:
| Дата: | 2005 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2005
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/156620 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A note to my paper “Generalized equivalence of collections of matrices and common divisors of matrices” / V.M. Petrychkovych // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 2. — С. 94–95. — Бібліогр.: 1 назв. — англ. |
Репозитарії
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Algebra and Discrete Mathematics A SHORT NOTE
Number 2. (2005). pp. 94 – 95
c© Journal “Algebra and Discrete Mathematics”
A note to my paper “Generalized equivalence of
collections of matrices and common divisors of
matrices”
Vasyl‘ M. Petrychkovych
Abstract. We correct some misprints and other oversights
in the paper mentioned in the title.
In this note we correct some misprints and other oversights in the
paper [1].
On p. 86 in [1], line 3 a label (2) of the formula
DA = ΦΨ = diag(ϕ1, . . . , ϕs, 0, . . . , 0)diag(ψ1, . . . , ψt, 0, . . . , 0)
was dropped. So this formula must have number (2). Then beginning
from p. 87 the numbers of formulas (2) - (8) should be replased by (3) -
(9). Note that in the text of the paper the citations on the formulas do
not change.
In the statements of theorems 1,3 and of corollaries 1,2 it should mean
that Ψ = diag(ψ1, . . . , ψt, 0, . . . , 0) is d-matrix, i.e. ψ1|ψ2| · · · |ψt. Thus in
Theorem 1 the phrase "Let A ∈M(m,n,R), m ≤ n" should be prolonged
as follows: "and the canonical diagonal form DA of the matrix A can be
represented in the form (2), where Ψ is d-matrix, t ≤ s and rangΦ = r
or rangΦ = m and ϕr+1 = ϕr+2 = · · · = ϕm." Also in Theorem 3 after
the formula (6) "DA = ΦΨ, DA = ΦΛ" it should be writed "where Ψ is
d-matrix and s = r or s = m and ϕr+1 = ϕr+2 = · · · = ϕm."
References
[1] V. M. Petrychkovych, Generalized equivalence of collections of matrices and com-
mon divisors of matrices, Algebra and Discrete Mathematics, N. 2, 2004, pp. 84-91.
2000 Mathematics Subject Classification: 15A33, 15A21, 15A23.
Key words and phrases: collection of matrices, generalized equivalence, canon-
ical diagonal form, common divisors.
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.V. M. Petrychkovych 95
Contact information
V. M.
Petrychkovych
Department of Algebra, Pidstryhach Insti-
tute for Applied Problems of Mechanics and
the Mathematics National Academy of Sci-
ences of Ukraine, 3B Naukova Str., Lviv,
79053, Ukraine
E-Mail: vas_petrych@yahoo.com,
vpetrych@iapmm.lviv.ua
Received by the editors: 02.09.2004
and final form in 30.06.2005.
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| spelling |
nasplib_isofts_kiev_ua-123456789-1566202025-02-09T13:29:16Z A note to my paper “Generalized equivalence of collections of matrices and common divisors of matrices” Petrychkovych, V.M. We correct some misprints and other oversights in the paper mentioned in the title. 2005 Article A note to my paper “Generalized equivalence of collections of matrices and common divisors of matrices” / V.M. Petrychkovych // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 2. — С. 94–95. — Бібліогр.: 1 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 15A33, 15A21, 15A23. https://nasplib.isofts.kiev.ua/handle/123456789/156620 en Algebra and Discrete Mathematics application/pdf Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We correct some misprints and other oversights
in the paper mentioned in the title. |
| format |
Article |
| author |
Petrychkovych, V.M. |
| spellingShingle |
Petrychkovych, V.M. A note to my paper “Generalized equivalence of collections of matrices and common divisors of matrices” Algebra and Discrete Mathematics |
| author_facet |
Petrychkovych, V.M. |
| author_sort |
Petrychkovych, V.M. |
| title |
A note to my paper “Generalized equivalence of collections of matrices and common divisors of matrices” |
| title_short |
A note to my paper “Generalized equivalence of collections of matrices and common divisors of matrices” |
| title_full |
A note to my paper “Generalized equivalence of collections of matrices and common divisors of matrices” |
| title_fullStr |
A note to my paper “Generalized equivalence of collections of matrices and common divisors of matrices” |
| title_full_unstemmed |
A note to my paper “Generalized equivalence of collections of matrices and common divisors of matrices” |
| title_sort |
note to my paper “generalized equivalence of collections of matrices and common divisors of matrices” |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2005 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/156620 |
| citation_txt |
A note to my paper “Generalized equivalence of collections of matrices and common divisors of matrices” / V.M. Petrychkovych // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 2. — С. 94–95. — Бібліогр.: 1 назв. — англ. |
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Algebra and Discrete Mathematics |
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2025-11-26T05:11:29Z |
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