A cikin wannan ɗaba'ar, za mu yi la'akari da ma'ana da manyan abubuwan matrix tare da misalai, iyakarsa, da kuma samar da taƙaitaccen tarihin tarihi game da ci gaban ka'idar matrix.
Ma'anar Matrix
matrix wani nau'i ne na tebur mai rectangular wanda ya ƙunshi layuka da ginshiƙai masu ɗauke da wasu abubuwa.
Girman Matrix yana saita adadin layuka da ginshiƙai, waɗanda haruffa ke nunawa m и n, bi da bi. Teburin da kansa an tsara shi da maƙallan madaukai (wani lokaci madauri mai murabba'i) ko layi ɗaya/biyu masu kamanceceniya da juna.
Ana nuna matrix da babban harafi A, kuma tare da alamar girmansa - Amn. Ana nuna misali a ƙasa:
Aikace-aikacen matrices a cikin lissafi
Ana amfani da matrices don rubutawa da warwarewa ko tsarin daidaitattun daidaito.
Abubuwan Matrix
Don nuna abubuwan da ke cikin matrix, ana amfani da daidaitaccen bayanin kula aij, ina:
- i - adadin layin da ke ɗauke da abin da aka bayar;
- j – bi da bi, shafi lambar.
Misali, ga matrix na sama:
- a24 = 1 (jere na biyu, shafi na hudu);
- a32 = 16 (jere na uku, shafi na biyu).
Rows
Idan duk abubuwan da ke cikin layin matrix daidai suke da sifili, to ana kiran irin wannan layin null (haske da kore).
In ba haka ba, layin shine nonzero (wanda aka haskaka da ja).
Diagonal
Ana kiran diagonal ɗin da aka zana daga kusurwar hagu na sama na matrix zuwa ƙasan dama babba.
Idan an zana diagonal daga ƙasa hagu zuwa sama dama, ana kiran shi Gida.
Bayanan tarihi
"Dandalin sihiri" - a karkashin wannan sunan, an fara ambaton matrices a tsohuwar kasar Sin, kuma daga baya a cikin malaman lissafin Larabawa.
A cikin 1751 masanin lissafin Swiss Gabriel Cramer ya buga "Dokar Kramer"ana amfani da su don warware tsarin daidaita algebraic na layi (SLAE). Kusan a lokaci guda, "hanyar Gauss" ta bayyana don magance SLAE ta hanyar kawar da masu canji (marubuci shine Carl Friedrich Gauss).
Mahimman gudumawa ga ci gaban ka'idar matrix suma sun samu ta hanyar irin su William Hamilton, Arthur Cayley, Karl Weierstrass, Ferdinand Frobenius da Marie Enmond Camille Jordan. Wannan kalmar "matrix" a cikin 1850 James Sylvester ya gabatar da shi.