ORTONORMALISASI VEKTOR BASIS DENGAN PROSES GRAM SCHMIDT

Irma Budi Wardani; Hartanto Sunardi

doi:10.36456/buanamatematika.v5i2:.391

Authors

Irma Budi Wardani Pendidikan Matematika, Fakultas Keguruan dan Ilmu Pendidikan, Universitas PGRI Adi Buana Surabaya Author
Hartanto Sunardi Pendidikan Matematika, Fakultas Keguruan dan Ilmu Pendidikan, Universitas PGRI Adi Buana Surabaya Author

DOI:

https://doi.org/10.36456/buanamatematika.v5i2:.391

Abstract

Gram schmidt process is one of linear algebra roles that associated by basis vector. This thesis aims to determine theoretically step by step in the process of gram schmidt.

Gram schmidt process is a method that used to convert an arbitrary basis vector into an orthogonal basis vector. After orthogonal basis vector had been obtained, the orthogonal basis vector was compiled into an orthonormal basis through step by step.

A vector on will be expressed as a basis vector if the vector if the vectors in are linear independently and spinning against . And a basis vector can be expressed as a set of orthonormal vectors, then the vector is an orthogonalvector and has norm = 1. If the basis vector has norm 1, to normalize the basis vector by using gram schmidt process.

Keywords: vector base, ortonormalisasi, gram schmidt proses.

Downloads

Download data is not yet available.

References

Anton, Howard. 1987. Aljabar Linear Elementer. Edisi kelima. Jakarta : Erlangga

Anton, Howard. 2000. Dasar-dasar Aljabar Linear. Jilid 1. Tangerang : Bina Rupa Aksara

Budhi, Wono Setya. 1995. Aljabar Linear. Jakarta : Gramedia Pustaka Utama

Gunawan, Hendra. 2007. Naskah Pidato. Institusi Tehnologi Bandung. http://personal.fmipa.itb.ac.id/hgunawan. Diakses 2 Agustus 2014 pukul 10:02

Hefferon, Jim. 2014. Linear Algebra. http://joshua.smcvt.edu/linearalgebra. Diakses tanggal 23 Juli 2014 pukul 20:26

http://hariono5a.files.wordpress.com/2011/01/ruang-berdimensi-n-euclidis Diakses 2 Agustus 2014 pukul 22:30

http://mathematics.its.ac.id/module/ Diakses 23 Juli 2014 pukul 03:41

https://asimtot.files.wordpress.com/2010/06/aljabar-linier-elementer Diakses 23 Juli2014 pukul 21:25

Karso, 2006. Penerapan Aljabar Linear. http://file.upi.edu/Diektori Diakses tanggal 23 Juli 2014 pukul 20:19

Leon, Steven J. 1998. Aljabar Linear dan Aplikasinya. Edisi ke-5. Jakarta : Erlangga

Lipschutz, Seymour. 1991. Schaum Outline of theory and problems of linear algebra second edition. Unitet states of America

Rorres, Anton. 2004. Aljabar Linear Versi Aplikasi. Edisi Kedelapan. Jilid 1. Jakarta : Erlangga

Shiddiq, M.Mahfuzh. 2013. Ortogonalitas – P Di Ruang Norm – n. Vol.4.No.1. http://repository.library.uksw.edu. Diakses tanggal 2 Agustus pukul 10:09

Sukmana, Agus. 2006. Pendekatan Aljabar Linear Untuk Kompresi Data Dengan Wavelet. Jurnal Ilmiah Ilmu Komputer. Vol. 4. No. 3. September 2006. pp. 185-196.

Ufyanty,ulfi Iffanyl. 2010. Hasil Kali Dalam-n Pada Ruang Vektor-n Atas Lapangan. Skripsi. Universitas Negeri Surabaya

Wahyuni, Sri. 2004. Aljabar Linear dan Aplikasinya. Naskah Pidato. Universitas Gajah Mada. http://lib.ugm.ac.id/digitasi. Diakses 24 Agustus 2014 pukul 03:48