Karyati (2006) Sifat Pasangan Adjoin Relatif Terhadap Bentuk Bilinear. Seminar Nasional MIPA 2006: Penelitian, Pendidikan, dan Penerapan MIPA serta Peranannya dalam Peningkatan Keprofesionalan Pendidik dan Tenaga Kependidikan. ISSN 979-99314-1-X
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Abstract
Let X and Y be vector spaces over a field K , then be constructed a bilinear form B : X × Y ⎯ ⎯→ K . This paper discuss the properties of adjoin pairs with respect to the bilinear form B . The result show that : ( f , g ) is an Adjoin pairs if and only if f o B ∗ = B ∗ o g ∗ , g ∗ ∈ L( Y ∗ ) defined as (t ) g ∗ = g o t , ∀t ∈ Y ∗ ; ( f , g ) is Adjoin pairs if and only if g o B ∗ = B∗ o f ∗ , f ∗ ∈ L (X ∗ ) defined as (t ) f ∗ = f o t , ∀t ∈ X ∗ ; If B : X × Y → K is a non degenerate bilinear form and the dimension of X and Y are finite, then for every ∧ f ∈ L( X ) there is g ∈ L( Y ) such that ( f , g ) is Adjoin pairs, N (g ) = R ( f ) and ∧ R( g ) = N ( f ) . As the corollary , for every g ∈ L( Y ) there is f ∈ L( X ) such that ( f , g ) is ∧ ∧ Adjoin pairs, N ( g ) = R( f ) and R (g ) = N ( f ) . Keywords: Bilinear form, non degenerate, adjoin pairs
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Bilinear form, non degenerate, adjoin pairs |
| Subjects: | Prosiding > Seminar Nasional MIPA 2006 |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA) > Pendidikan Matematika > Matematika Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA) > Pendidikan Matematika > Pendidikan Matematika |
| Depositing User: | Eprints |
| Date Deposited: | 03 Feb 2015 00:42 |
| Last Modified: | 08 Mar 2019 06:16 |
| URI: | http://eprints.uny.ac.id/id/eprint/11986 |
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