[ABSTRAK
Dalam tesis ini diperkenalkan ruang hasil kali dalam-n dan ruang norm-nsebagai perluasan dari ruang hasil kali dalam dan ruang norm. Setiap ruang hasilkali dalam dapat dilengkapi dengan suatu hasil kali dalam-n sederhanahx0;x1jx2;


;xni =hx0;x1i hx0;x2i


hx0;xnihx2;x1i hx2;x2i


hx2;xni ....... . . ...hxn;x1i hxn;x2i


hxn;xni:Hasil kali dalam-n sederhana ini menginduksi suatu norm-n standarkx1;


;xnk =phx1;x1jx2;


;xni;yang tak lain merupakan determinan Gram yang merupakan kuadrat dari volumedari paralelotop berdimensi-n yang dibangun oleh x1;


;xn.Tugas akhir ini membahas tentang sudut antara dua subruang dari suatu ruanghasil kali dalam-n dan representasinya secara geometris. Lebih lanjut, dipelajarihubungannya dengan sudut-sudut kanonik yang selama ini telah digunakan untukmendeskripsikan sudut antara dua ruang.

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ABSTRACT
The definitions of n-inner product space and n-normed space as generalizationsof inner product space and normed space are introduced. Every inner productspace can form an n-inner product space with a simple n-inner producthx0;x1jx2;


;xni =hx0;x1i hx0;x2i


hx0;xnihx2;x1i hx2;x2i


hx2;xni ....... . . ...hxn;x1i hxn;x2i


hxn;xni:The simple n-inner product induces a standard n-normkx1;


;xnk =phx1;x1jx2;


;xni;which is actually the Gram determinant which represents the square root of thevolume of the n-dimensional parallelotope generated by x1;


;xn.This thesis discussed the angle between subspaces of an n-inner product spaceand its geometrical representation. Moreover, its relation to canonical angles,which has been used for describing the angles between two subspaces, is observedtoo.;The definitions of n-inner product space and n-normed space as generalizationsof inner product space and normed space are introduced. Every inner productspace can form an n-inner product space with a simple n-inner producthx0;x1jx2;


;xni =hx0;x1i hx0;x2i


hx0;xnihx2;x1i hx2;x2i


hx2;xni ....... . . ...hxn;x1i hxn;x2i


hxn;xni:The simple n-inner product induces a standard n-normkx1;


;xnk =phx1;x1jx2;


;xni;which is actually the Gram determinant which represents the square root of thevolume of the n-dimensional parallelotope generated by x1;


;xn.This thesis discussed the angle between subspaces of an n-inner product spaceand its geometrical representation. Moreover, its relation to canonical angles,which has been used for describing the angles between two subspaces, is observedtoo., The definitions of n-inner product space and n-normed space as generalizationsof inner product space and normed space are introduced. Every inner productspace can form an n-inner product space with a simple n-inner producthx0;x1jx2;


;xni =hx0;x1i hx0;x2i


hx0;xnihx2;x1i hx2;x2i


hx2;xni ....... . . ...hxn;x1i hxn;x2i


hxn;xni:The simple n-inner product induces a standard n-normkx1;


;xnk =phx1;x1jx2;


;xni;which is actually the Gram determinant which represents the square root of thevolume of the n-dimensional parallelotope generated by x1;


;xn.This thesis discussed the angle between subspaces of an n-inner product spaceand its geometrical representation. Moreover, its relation to canonical angles,which has been used for describing the angles between two subspaces, is observedtoo.]