ORTHOGONALITAS-BIRKHOFF

BESTARI RATNA AYU SAHESTI, Dr. Atok Zulijanto, M.Si.

2014 | Skripsi | MATEMATIKA

Pada skripsi ini akan dibahas orthogonalitas pada ruang bernorma real yaitu orthogonalitas menurut G.Birkhoff. Orthogonalitas-Birkhoff merupakan perumuman orthogonalitas di ruang inner product. Pengertian orthogonalitas pada ruang inner product real ekuivalen dengan orthogonalitas-Birkhoff. Selain itu, terdapat konsep yang lebih lemah daripada inner product yaitu semi-inner product Lumer- Giles dan semi-inner product superior-inferior. Pada skripsi ini dipelajari juga hubungan orthogonalitas-Birkhoff dengan orthogonalitas di ruang semi-inner product Lumer-Giles dan ruang semi-inner product superior-inferior. Pada akhir skripsi ini dibahas hubungan orthogonalitas-Birkhoff dengan fungsional linear.

In this final project, we study on an orthogonality in real normed spaces in the sense of Birkhoff. The Brikhoff-orthogonality is a generalization of the orthogonality in inner product spaces. Definition of orthogonality in a real inner product space equivalent to the Birkhoff-orthogonality. There are weaker concepts of inner product that are Lumer-Giles semi-inner product and superior-inferior semi-inner product. In this final project we also study relation between Birkhoff-orthogonality and orthogonality in Lumer-Giles semi-inner products and superior-inferior semiinner product. At the end, we present the relation between Birkhoff-orthogonality and linear functional.

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