Aljabar linèar

Aljabar linèar èngghi panèka pangajhârân matematika se angajhâri ruang vektor bân pamètaan linèar. ^[1] Sacara èlèmènter aljabar linèar angajhâri tèknik-tèknik komputasional ḍâlem mamarè sistem persamaan linèar akadhi $a_{1}x_{1}+\cdots +a_{n}x_{n}=b,$ pamètaan linèar akadhi $(x_{1},\ldots ,x_{n})\mapsto a_{1}x_{1}+\cdots +a_{n}x_{n},$ bân rèprèsèntasinah ḍâlem ruang vèktor sanajjhân jughân sareng matriks. ^[2]^[3]^[4]

Aljabar linèar Andi' peran penting e sakabbhina pangajhârân matematika. Mènangka conto aljabar linèar dâddhi dâsar ḍâlâam ajellassaghi gèomètri sacara modern, tamaso' ḍâlâm ngartèaghi objèk-objèk dhâsar akhadi garis, bidhâng, bân rotasi.

Sajhârâ

Mamarè sabâghiyân persamaan linèar sacara abhârângan adâddhi bâghiyân penting ḍâlem aljabar linèar. Prosedur ḍâlem mamarèaghi masalah kasebhut sè samangkèn èkennal mènangka Èliminasi Gauss dhâ'-adhâ' meddul ḍâlem bab bellu': Array Persegi Panjang è bhuku matematika Cina Lajuh Sembilan Bab Dalam Seni Matematika. Bhuku panèka aghâmbhâraghi 18 masalah bik-dhibik ngalèbbhâaghi sampè' lèma' persamaan. ^[5]

Sistem persamaan linèar berkembang è Èropa abhârângan sareng èkennalaghinah konsèp koordinat ḍâlem gèomètri, sareng René Descartes è taon 1637.

È perkembangan saterossa, dèterminan èghunaaghi ka'angghuy mamarè sistem persamaan linèar sacara sistematis. Mètode panèka dhâ'-adhâ' èpatimbangaghi sareng Leibiniz è taon 1693. È taon 1750 Gabriel Cramer aghunaahi dèterminan ka'angghuy angasèlaghi solusi [sistem persamaan linèar]] sacara jellas, aghunaahi mètode sè samangkèn èkennal sareng atoran Cramer. Gauss jughân ajellassaghi lebbi terros tentang mètode èliminasi, sè awalla ècatet mènangka setting kamajuwân ḍâlem gèodèsi. ^[6]

Rèfèrènsi

↑ Axler, Sheldon Jay (2024). Linear Algebra Done Right. Undergraduate Texts in Mathematics. Cham: Springer Nature. ISBN 978-3-031-41025-3.
↑ Banerjee, Sudipto; Roy, Anindya (2014), Linear Algebra and Matrix Analysis for Statistics, Texts in Statistical Science (1st ed.), Chapman and Hall/CRC, ISBN 978-1420095388
↑ Strang, Gilbert (July 19, 2005), Linear Algebra and Its Applications (4th ed.), Brooks Cole, ISBN 978-0-03-010567-8
↑ Weisstein, Eric. "Linear Algebra". From MathWorld--A Wolfram Web Resource. Wolfram. Retrieved 16 April 2012.
↑ Hart, Roger (2010). The Chinese Roots of Linear Algebra. JHU Press. ISBN 9780801899584.
↑ Vitulli, Marie. "A Brief History of Linear Algebra and Matrix Theory". Department of Mathematics. University of Oregon. Archived from the original on 2012-09-10. Retrieved 2014-07-08.

[1] Axler, Sheldon Jay (2024). Linear Algebra Done Right. Undergraduate Texts in Mathematics. Cham: Springer Nature. ISBN 978-3-031-41025-3.

[2] Banerjee, Sudipto; Roy, Anindya (2014), Linear Algebra and Matrix Analysis for Statistics, Texts in Statistical Science (1st ed.), Chapman and Hall/CRC, ISBN 978-1420095388

[3] Strang, Gilbert (July 19, 2005), Linear Algebra and Its Applications (4th ed.), Brooks Cole, ISBN 978-0-03-010567-8

[4] Weisstein, Eric. "Linear Algebra". From MathWorld--A Wolfram Web Resource. Wolfram. Retrieved 16 April 2012.

[5] Hart, Roger (2010). The Chinese Roots of Linear Algebra. JHU Press. ISBN 9780801899584.

[Vitulli,_Marie-6] Vitulli, Marie. "A Brief History of Linear Algebra and Matrix Theory". Department of Mathematics. University of Oregon. Archived from the original on 2012-09-10. Retrieved 2014-07-08.

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