Converting immanants on singular symmetric matrices
Let Σ n (F) denote the space of all n × n symmetricmatrices over the complex field F, and χ be an irreducible character of S n and d χ the immanant associated with χ. The main objective of this paper is to prove that the maps Φ: Σ n (F) → Σ n (F) satisfying d χ (Φ( A ) + α Φ( B )) = det ( A + αB ) f...
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| Veröffentlicht in: | Lobachevskii journal of mathematics 2017-07, Vol.38 (4), p.630-636 |
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| container_title | Lobachevskii journal of mathematics |
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| creator | Duffner, M. A. Guterman, A. E. |
| description | Let Σ
n
(F) denote the space of all
n
×
n
symmetricmatrices over the complex field F, and χ be an irreducible character of
S
n
and
d
χ
the immanant associated with χ. The main objective of this paper is to prove that the maps Φ: Σ
n
(F) → Σ
n
(F) satisfying
d
χ
(Φ(
A
) +
α
Φ(
B
)) =
det
(
A
+
αB
) for all singular matrices
A
,
B
∈ Σ
n
(F) and all scalars
α
∈ F are linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on the set of all symmetric matrices. |
| doi_str_mv | 10.1134/S1995080217040060 |
| format | Article |
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n
(F) denote the space of all
n
×
n
symmetricmatrices over the complex field F, and χ be an irreducible character of
S
n
and
d
χ
the immanant associated with χ. The main objective of this paper is to prove that the maps Φ: Σ
n
(F) → Σ
n
(F) satisfying
d
χ
(Φ(
A
) +
α
Φ(
B
)) =
det
(
A
+
αB
) for all singular matrices
A
,
B
∈ Σ
n
(F) and all scalars
α
∈ F are linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on the set of all symmetric matrices.</description><identifier>ISSN: 1995-0802</identifier><identifier>EISSN: 1818-9962</identifier><identifier>DOI: 10.1134/S1995080217040060</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Algebra ; Analysis ; Conversion ; Geometry ; Mathematical analysis ; Mathematical Logic and Foundations ; Mathematics ; Mathematics and Statistics ; Matrices (mathematics) ; Matrix methods ; Probability Theory and Stochastic Processes ; Scalars</subject><ispartof>Lobachevskii journal of mathematics, 2017-07, Vol.38 (4), p.630-636</ispartof><rights>Pleiades Publishing, Ltd. 2017</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-bfa51ca24bee6561fc0a4238972f44c2eca68636812c3635a00c6ca2897fd83f3</citedby><cites>FETCH-LOGICAL-c316t-bfa51ca24bee6561fc0a4238972f44c2eca68636812c3635a00c6ca2897fd83f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S1995080217040060$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S1995080217040060$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>315,781,785,27929,27930,41493,42562,51324</link.rule.ids></links><search><creatorcontrib>Duffner, M. A.</creatorcontrib><creatorcontrib>Guterman, A. E.</creatorcontrib><title>Converting immanants on singular symmetric matrices</title><title>Lobachevskii journal of mathematics</title><addtitle>Lobachevskii J Math</addtitle><description>Let Σ
n
(F) denote the space of all
n
×
n
symmetricmatrices over the complex field F, and χ be an irreducible character of
S
n
and
d
χ
the immanant associated with χ. The main objective of this paper is to prove that the maps Φ: Σ
n
(F) → Σ
n
(F) satisfying
d
χ
(Φ(
A
) +
α
Φ(
B
)) =
det
(
A
+
αB
) for all singular matrices
A
,
B
∈ Σ
n
(F) and all scalars
α
∈ F are linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on the set of all symmetric matrices.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Conversion</subject><subject>Geometry</subject><subject>Mathematical analysis</subject><subject>Mathematical Logic and Foundations</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Matrices (mathematics)</subject><subject>Matrix methods</subject><subject>Probability Theory and Stochastic Processes</subject><subject>Scalars</subject><issn>1995-0802</issn><issn>1818-9962</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kEFLAzEQhYMoWKs_wNuC59WZJDtNjrKoFQoe1POSxqRs6WZrsiv035uyHgTxNMO8772Bx9g1wi2ikHevqHUFCjguQAIQnLAZKlSl1sRP857l8qifs4uUtgCcE9GMiboPXy4ObdgUbdeZYMKQij4UKV_GnYlFOnSdG2Jri84ch0uX7MybXXJXP3PO3h8f3upluXp5eq7vV6UVSEO59qZCa7hcO0cVobdgJBdKL7iX0nJnDSkSpJBbQaIyAJYynwH_oYQXc3Yz5e5j_zm6NDTbfowhv2xQoyaSyFWmcKJs7FOKzjf72HYmHhqE5thN86eb7OGTJ2U2bFz8lfyv6Rvo5WTy</recordid><startdate>20170701</startdate><enddate>20170701</enddate><creator>Duffner, M. A.</creator><creator>Guterman, A. E.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20170701</creationdate><title>Converting immanants on singular symmetric matrices</title><author>Duffner, M. A. ; Guterman, A. E.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-bfa51ca24bee6561fc0a4238972f44c2eca68636812c3635a00c6ca2897fd83f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Conversion</topic><topic>Geometry</topic><topic>Mathematical analysis</topic><topic>Mathematical Logic and Foundations</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Matrices (mathematics)</topic><topic>Matrix methods</topic><topic>Probability Theory and Stochastic Processes</topic><topic>Scalars</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Duffner, M. A.</creatorcontrib><creatorcontrib>Guterman, A. E.</creatorcontrib><collection>CrossRef</collection><jtitle>Lobachevskii journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Duffner, M. A.</au><au>Guterman, A. E.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Converting immanants on singular symmetric matrices</atitle><jtitle>Lobachevskii journal of mathematics</jtitle><stitle>Lobachevskii J Math</stitle><date>2017-07-01</date><risdate>2017</risdate><volume>38</volume><issue>4</issue><spage>630</spage><epage>636</epage><pages>630-636</pages><issn>1995-0802</issn><eissn>1818-9962</eissn><abstract>Let Σ
n
(F) denote the space of all
n
×
n
symmetricmatrices over the complex field F, and χ be an irreducible character of
S
n
and
d
χ
the immanant associated with χ. The main objective of this paper is to prove that the maps Φ: Σ
n
(F) → Σ
n
(F) satisfying
d
χ
(Φ(
A
) +
α
Φ(
B
)) =
det
(
A
+
αB
) for all singular matrices
A
,
B
∈ Σ
n
(F) and all scalars
α
∈ F are linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on the set of all symmetric matrices.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S1995080217040060</doi><tpages>7</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1995-0802 |
| ispartof | Lobachevskii journal of mathematics, 2017-07, Vol.38 (4), p.630-636 |
| issn | 1995-0802 1818-9962 |
| language | eng |
| recordid | cdi_proquest_journals_1919664128 |
| source | SpringerNature Journals |
| subjects | Algebra Analysis Conversion Geometry Mathematical analysis Mathematical Logic and Foundations Mathematics Mathematics and Statistics Matrices (mathematics) Matrix methods Probability Theory and Stochastic Processes Scalars |
| title | Converting immanants on singular symmetric matrices |
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