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  3. Formalized Mathematics
  4. Formalized Mathematics, 2003, Volume 11, Issue 1

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/21478
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    Pole DCWartośćJęzyk
    dc.contributor.authorKotowicz, Jarosław-
    dc.date.accessioned2026-11-09T13:16:55Z-
    dc.date.available2026-11-09T13:16:55Z-
    dc.date.issued2003-
    dc.identifier.citationFormalized Mathematics, Volume 11, Issue 1, Pages 87-98pl
    dc.identifier.issn1426-2630-
    dc.identifier.urihttp://hdl.handle.net/11320/21478-
    dc.description.abstractIn the article we present antilinear functionals, sesquilinear and hermitan forms. We prove Schwarz and Minkowski inequalities, and Parallelogram Law for non-negative hermitan form. The proof of Schwarz inequality is based on [14]. The incorrect proof of this fact can be found in [11]. The construction of scalar product in quotient vector space from non-negative hermitan functions is the main result of the article.pl
    dc.description.sponsorshipThis work has been partially supported by TRIAL-SOLUTION grant IST-2001-35447 and SPUB-M grant of KBN.-
    dc.language.isoenpl
    dc.publisherUniversity of Białystokpl
    dc.rightsCC BY-SA 4.0-
    dc.rights.urihttps://creativecommons.org/licenses/by-sa/4.0/-
    dc.titleHermitan Functionals. Canonical Construction of Scalar Product in Quotient Vector Spacepl
    dc.typeArticlepl
    dc.rights.holder© 2003 University of Białystokpl
    dc.rights.holderThis work is licensed under the Creative Commons License.pl
    dc.description.AffiliationUniversity of Białystokpl
    dc.description.referencesJózef Białas. Group and field definitions. Formalized Mathematics, 1(3):433–439, 1990.pl
    dc.description.referencesCzesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507–513, 1990.pl
    dc.description.referencesCzesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55–65, 1990.pl
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    dc.description.referencesCzesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47–53, 1990.pl
    dc.description.referencesKrzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35–40, 1990.pl
    dc.description.referencesJarosław Kotowicz. Monotone real sequences. Subsequences. Formalized Mathematics, 1(3):471–475, 1990.pl
    dc.description.referencesJarosław Kotowicz. Bilinear functionals in vector spaces. Formalized Mathematics, 11(1):69–86, 2003.pl
    dc.description.referencesJarosław Kotowicz. Quotient vector spaces and functionals. Formalized Mathematics, 11(1):59–68, 2003.pl
    dc.description.referencesEugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335–342, 1990.pl
    dc.description.referencesKrzysztof Maurin. Analiza, II, volume 70 of Biblioteka Matematyczna. PWN - Warszawa, 1991.pl
    dc.description.referencesAnna Justyna Milewska. The field of complex numbers. Formalized Mathematics, 9(2):265–269, 2001.pl
    dc.description.referencesAnna Justyna Milewska. The Hahn Banach theorem in the vector space over the field of complex numbers. Formalized Mathematics, 9(2):363–371, 2001.pl
    dc.description.referencesWalter Rudin. Real and Complex Analysis. Mc Graw-Hill, Inc., 1974.pl
    dc.description.referencesAndrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115–122, 1990.pl
    dc.description.referencesAndrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9–11, 1990.pl
    dc.description.referencesAndrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445–449, 1990.pl
    dc.description.referencesWojciech A. Trybulec. Subspaces and cosets of subspaces in vector space. Formalized Mathematics, 1(5):865–870, 1990.pl
    dc.description.referencesWojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291–296, 1990.pl
    dc.description.referencesZinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67–71, 1990.pl
    dc.description.referencesEdmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181–186, 1990.pl
    dc.identifier.eissn1898-9934-
    dc.description.volume11pl
    dc.description.issue1pl
    dc.description.firstpage87pl
    dc.description.lastpage98pl
    dc.identifier.citation2Formalized Mathematicspl
    Występuje w kolekcji(ach):Formalized Mathematics, 2003, Volume 11, Issue 1

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