Subruang Invarian Oleh Transformasi Linier Khusus

Aini, Hikmatul (2003) Subruang Invarian Oleh Transformasi Linier Khusus. Undergraduate thesis, FMIPA Undip.

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Abstract

Misalkan C" adalah ruang vektor kompleks berdimensi berhingga (dengan dim (C") = dan T: —> adalah suatu transformasi liner. Suatu subruang M c dikatakan invarian untuk transformasi linier T atau disingkat T¬invarian jika untuk setiap XE M berlaku T(x) E M. Dengan kata lain, M invarian untuk T jika peta dart M atas T tennuat di M, yaitu T(M) c M. Dapat diperlihatkan bahwa subruang yang direntang oleh vektor-vektor eigen dan rantai jordan oleh transformasi tinier T adalah subruang T-invarian. Dan suatu subruang dart ruang vektor kompleks oleh beberapa transformasi linier khusus seperti transformasi similar, transformasi adjoint, dan transformasi self adjoint merupakan subruang invarian. Let C" is a complex vector spaces with finite dimensional (dim (C") = and T: C" C" be a linear transformation. A subspace Mc C" is called invariant for the linear transformation T, or T-invariant T(x) e NI for eve!), vector xE M. In other words, M is invariant for T means that the image of M under T is contained in M; ?7M) c M. It can be shown that a subspace which spanned by eigen vectors and Jordan chains is a T-invariant subspaces. And the subspaces of complex vector space by some special linear transformation such as similar transformation, adjoint transformation, and self adjoin! transformation is an invariant subspace

Item Type:Thesis (Undergraduate)
Subjects:Q Science > QA Mathematics
Divisions:Faculty of Science and Mathematics > Department of Mathematics
ID Code:32244
Deposited By:Mr UPT Perpus 1
Deposited On:04 Jan 2012 09:27
Last Modified:04 Jan 2012 09:27

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