M aikace-aikace da kuma gano da kishiya matrix

Matrix - a tebur, wanda aka cika da wani sa na lambobin a wani tsari. Wannan lokaci da aka buga fice Birtaniya masanin kimiyya ne msar tambayar James Sylvester. Shi ne daya daga cikin wadanda suka kafa ka'idar aikace-aikace na wadannan ilmin lissafi abubuwa.

Don kwanan wata, da suka da aka yi amfani da ko'ina a lokacin daban-daban da lissafin, wadda ake bisa wani Hanyar kamar, misali, gano da kishiya matrix a cikin daban-daban rassan mutum aiki. Wannan hanyar dogara ne a kan kayyade unknown sigogi daban-daban na tsarin na lissafai da aka sau da yawa amfani a lokacin da tattalin arziki da lissafin.

Akwai da wadannan lokuta na musamman wadannan ilmin lissafi aka gyara: ƙananan baƙaƙe, wani shafi, sifili, square, diagonal, guda. Ƙaramin baki kunshi daya kawai jere na abubuwa, da kuma wani shafi - wata guda shafi na lambobin. Zero - duk da abubuwa daidai da 0. A ilmin lissafi square da kashi yawan ginshikan daidaita da yawan layuka. Bi da bi, a cikin diagonal, located a kan babban diagonal abubuwa daban-daban daga "0", da sauran shi ya zama daidai "0". Identity - shi ne mai subspecies na diagonal matrix. Ta kawai "1" ne located a kan babban diagonal.

Misalan matrices:

a cikinsa: A _k - a Generic lokaci, wani _ij - abubuwa,

(A) 2-th domin;

(B) - ƙananan baƙaƙe;

(A) -3-th domin;

(G) - Misalin 2-th domin naúrar tebur.

Har ila yau, akwai wani kishiya matrix, da definition wanda shi ne kamar haka. Lokacin da ta tara da asali tebur na feedback naúrar da aka samu. A iri-iri na dabarun da damar gano da kishiya matrix. Mafi sauki daga wadannan dogara ne a kan definition daga cikin determinant kuma cofactors (kuma wani lokacin ake magana a kai a matsayin determinant).

A determinant na matrix ne mai magana da wani _{11 22} -A _{12 21,} an nuna kamar haka: | A |. The sama dabara yana aiki ga wani tebur bisa ga na biyu domin. Duk wani dabara domin determinants na matrices na mafi girma domin. Wajibi yanayin ga wanzuwar da determinant - tebur ya zama square. A aikace, wannan kashi na wannan ka'idar aka fi amfani da irin wannan hanya a matsayin gano da kishiya matrix.

Na biyu muhimmin bangaren da cewa za a iya amfani da su sami dabi'u na ta abubuwa ne cofactor. Yana da aka lasafta ta da dabara: A _ij = (- 1) ^{i + j} * M _ij, a cikinsa M ne - wannan shi ne qananan. Da gaske - shi ne wani ƙarin determinant, wanda za a iya samu ta hanyar conceptually cire jere da shafi a cikin abin da aiki kashi ne located. Alal misali, a tebur, bisa ga na biyu domin, wanda aka nuna a baya a cikin rubutu, a cikin wani cell ₁₁ shi zai dace da algebraic kashi ₂₂ a.

Samun wani kishiya matrix muna yi a 3, saukarwa. A mataki na farko ne a tsare determinants. A mataki na gaba - duk cofactors, wanda aka sa'an nan a rubuce a daidai da ta fihirisa, kuma itace tebur cofactors. A karshe mataki na kishiya matrix samu ta hanyar binciken wanda ƙare da ya riɓaɓɓanya kowane algebraic tarawa a cikin determinant.

Da aka fi amfani matrix amfani da tattalin arziki lissafin. Tare da su taimako, za ka iya sauƙi, kuma da sauri aiwatar yawa bayani. A wannan yanayin, da karshen sakamakon za a gabatar a wani sauki fahimta daga form.

Wani fannin na mutum aiki, a cikin abin da matrix kuma samu babban amfani - wannan kwaikwaiyo 3D-images. Wadannan kayan aikin da ake batutuwa a cikin zamani kunshe-kunshe ga aiwatar da 3D-model da kuma ba da damar zanen kaya zuwa da sauri da kuma daidai cika da zama dole lissafin. Mafi shahararren wakilin irin wannan tsarin ne a kamfas-3D.

Wani shirin, wanda integrates da kayayyakin aiki, domin su gudanar da irin wannan lissafin, shi ne Microsoft Office, kuma mafi musamman - falle shirin Excel.