Ranked solutions of the matric equation A 1 X 1 = A 2 X 2
Let G F ( p z ) denote the finite field of p z elements. Let A 1 be s × m of rank r 1 and A 2 be s × n of rank r 2 with elements from G F ( p z ). In this paper, formulas are given for finding the number of X 1 , X 2 over G F ( p z ) which satisfy the matric equation A 1 X 1 = A 2 X 2 , where X 1 is...
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| Veröffentlicht in: | International journal of mathematics and mathematical sciences 1980-01, Vol.3 (2), p.293-304 |
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| container_title | International journal of mathematics and mathematical sciences |
| container_volume | 3 |
| creator | Porter, A. Duane Mousouris, Nick |
| description | Let
G
F
(
p
z
) denote the finite field of
p
z
elements. Let
A
1
be
s
×
m
of rank
r
1
and
A
2
be
s
×
n
of rank
r
2
with elements from
G
F
(
p
z
). In this paper, formulas are given for finding the number of
X
1
,
X
2
over
G
F
(
p
z
) which satisfy the matric equation
A
1
X
1
=
A
2
X
2
, where
X
1
is
m
×
t
of rank
k
1
, and
X
2
is
n
×
t
of rank
k
2
. These results are then used to find the number of solutions
X
1
, …,
X
n
,
Y
1
, …,
Y
m
,
m
,
n
> 1, of the matric equation
A
1
X
1
…
X
n
=
A
2
Y
1
…
Y
m
. |
| doi_str_mv | 10.1155/S016117128000021X |
| format | Article |
| fullrecord | <record><control><sourceid>crossref</sourceid><recordid>TN_cdi_crossref_primary_10_1155_S016117128000021X</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1155_S016117128000021X</sourcerecordid><originalsourceid>FETCH-LOGICAL-c90X-690f6314d68c5422a3cda3dab02bcbde05361066f915b640dafcbf01c9297df13</originalsourceid><addsrcrecordid>eNplT81KxDAYDKJgXX0Ab3mB6Pd9adLm4GFZ1BUWBN1DbyXND1Z3t5p0D769LXpzYJhhBgaGsWuEG0Slbl8BNWKFVMMEwuaEFajrSkBJ6pQVcy3m_pxd5PwOgDWRKph5sYeP4HkedsexHw6ZD5GPb4Hv7Zh6x8PX0c45X3LkzcS7ydHk6JKdRbvL4epPF2z7cL9drcXm-fFptdwIZ6AR2kDUEkuva6dKIiudt9LbDqhznQ-gpEbQOhpUnS7B2-i6COgMmcpHlAuGv7MuDTmnENvP1O9t-m4R2vl6---6_AF7X0h2</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Ranked solutions of the matric equation A 1 X 1 = A 2 X 2</title><source>Wiley Online Library Open Access</source><source>DOAJ Directory of Open Access Journals</source><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>Alma/SFX Local Collection</source><creator>Porter, A. Duane ; Mousouris, Nick</creator><creatorcontrib>Porter, A. Duane ; Mousouris, Nick</creatorcontrib><description>Let
G
F
(
p
z
) denote the finite field of
p
z
elements. Let
A
1
be
s
×
m
of rank
r
1
and
A
2
be
s
×
n
of rank
r
2
with elements from
G
F
(
p
z
). In this paper, formulas are given for finding the number of
X
1
,
X
2
over
G
F
(
p
z
) which satisfy the matric equation
A
1
X
1
=
A
2
X
2
, where
X
1
is
m
×
t
of rank
k
1
, and
X
2
is
n
×
t
of rank
k
2
. These results are then used to find the number of solutions
X
1
, …,
X
n
,
Y
1
, …,
Y
m
,
m
,
n
> 1, of the matric equation
A
1
X
1
…
X
n
=
A
2
Y
1
…
Y
m
.</description><identifier>ISSN: 0161-1712</identifier><identifier>EISSN: 1687-0425</identifier><identifier>DOI: 10.1155/S016117128000021X</identifier><language>eng</language><ispartof>International journal of mathematics and mathematical sciences, 1980-01, Vol.3 (2), p.293-304</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c90X-690f6314d68c5422a3cda3dab02bcbde05361066f915b640dafcbf01c9297df13</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,860,27901,27902</link.rule.ids></links><search><creatorcontrib>Porter, A. Duane</creatorcontrib><creatorcontrib>Mousouris, Nick</creatorcontrib><title>Ranked solutions of the matric equation A 1 X 1 = A 2 X 2</title><title>International journal of mathematics and mathematical sciences</title><description>Let
G
F
(
p
z
) denote the finite field of
p
z
elements. Let
A
1
be
s
×
m
of rank
r
1
and
A
2
be
s
×
n
of rank
r
2
with elements from
G
F
(
p
z
). In this paper, formulas are given for finding the number of
X
1
,
X
2
over
G
F
(
p
z
) which satisfy the matric equation
A
1
X
1
=
A
2
X
2
, where
X
1
is
m
×
t
of rank
k
1
, and
X
2
is
n
×
t
of rank
k
2
. These results are then used to find the number of solutions
X
1
, …,
X
n
,
Y
1
, …,
Y
m
,
m
,
n
> 1, of the matric equation
A
1
X
1
…
X
n
=
A
2
Y
1
…
Y
m
.</description><issn>0161-1712</issn><issn>1687-0425</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1980</creationdate><recordtype>article</recordtype><recordid>eNplT81KxDAYDKJgXX0Ab3mB6Pd9adLm4GFZ1BUWBN1DbyXND1Z3t5p0D769LXpzYJhhBgaGsWuEG0Slbl8BNWKFVMMEwuaEFajrSkBJ6pQVcy3m_pxd5PwOgDWRKph5sYeP4HkedsexHw6ZD5GPb4Hv7Zh6x8PX0c45X3LkzcS7ydHk6JKdRbvL4epPF2z7cL9drcXm-fFptdwIZ6AR2kDUEkuva6dKIiudt9LbDqhznQ-gpEbQOhpUnS7B2-i6COgMmcpHlAuGv7MuDTmnENvP1O9t-m4R2vl6---6_AF7X0h2</recordid><startdate>198001</startdate><enddate>198001</enddate><creator>Porter, A. Duane</creator><creator>Mousouris, Nick</creator><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>198001</creationdate><title>Ranked solutions of the matric equation A 1 X 1 = A 2 X 2</title><author>Porter, A. Duane ; Mousouris, Nick</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c90X-690f6314d68c5422a3cda3dab02bcbde05361066f915b640dafcbf01c9297df13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1980</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Porter, A. Duane</creatorcontrib><creatorcontrib>Mousouris, Nick</creatorcontrib><collection>CrossRef</collection><jtitle>International journal of mathematics and mathematical sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Porter, A. Duane</au><au>Mousouris, Nick</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Ranked solutions of the matric equation A 1 X 1 = A 2 X 2</atitle><jtitle>International journal of mathematics and mathematical sciences</jtitle><date>1980-01</date><risdate>1980</risdate><volume>3</volume><issue>2</issue><spage>293</spage><epage>304</epage><pages>293-304</pages><issn>0161-1712</issn><eissn>1687-0425</eissn><abstract>Let
G
F
(
p
z
) denote the finite field of
p
z
elements. Let
A
1
be
s
×
m
of rank
r
1
and
A
2
be
s
×
n
of rank
r
2
with elements from
G
F
(
p
z
). In this paper, formulas are given for finding the number of
X
1
,
X
2
over
G
F
(
p
z
) which satisfy the matric equation
A
1
X
1
=
A
2
X
2
, where
X
1
is
m
×
t
of rank
k
1
, and
X
2
is
n
×
t
of rank
k
2
. These results are then used to find the number of solutions
X
1
, …,
X
n
,
Y
1
, …,
Y
m
,
m
,
n
> 1, of the matric equation
A
1
X
1
…
X
n
=
A
2
Y
1
…
Y
m
.</abstract><doi>10.1155/S016117128000021X</doi><tpages>12</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0161-1712 |
| ispartof | International journal of mathematics and mathematical sciences, 1980-01, Vol.3 (2), p.293-304 |
| issn | 0161-1712 1687-0425 |
| language | eng |
| recordid | cdi_crossref_primary_10_1155_S016117128000021X |
| source | Wiley Online Library Open Access; DOAJ Directory of Open Access Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Alma/SFX Local Collection |
| title | Ranked solutions of the matric equation A 1 X 1 = A 2 X 2 |
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