Nā waiwai o ka'ōpū mai, a kona determinant

Waiwai o matrices - he nīnau i na mea he nui i i pilikia. No ia mea, ia mea pono e noonoo ia i loko o au mamuli.

'ōpū mai - he mau huinahń papaainaʻano, a me ka helu, a hehee wale. Nō hoʻi, i kēiaʻano o ka huapalapala o loa, a me nā kumu o kekahi 'ē' ole i ka palapala e like me he mau huinahń papaaina iloko olaila o kekahi mau helu o ka lalani a me kolamu. Kēia papaʻaina pono e puni i loko o parentheses. Ua hiki e poai brackets, parentheses, heʻahā like type a kauoha-type papalua brackets. A pau i ka helu i loko o ka'ōpū mai, ua kapaia - mua hehee ai, a me ka mea, i ko lakou mau wahi i loko o ka papaʻaina kahua. 'ōpū mai compulsorily i hoʻokohu ' ia e ka kapikala palapala o ka Lakina Hawaiʻi.

Waiwai o matrices a makemakika papa loaʻa kekahi mau, ao ke ano. Eia hou kekahi a me subtraction o matrices hehee ai ma ka hehee ai kŰlń ao pololei. Multiplication a me ka māhele o waho i ka laulā o ka maʻamau makemakika. E hoonui i kekahi mua a hiki i kekahi, ia mea pono e hoole i ka 'ike ma luna o ka scalar huina hoonui o ka maʻi lele i kekahi.

C = (he, b) = He 1 b. 1 + a 2 b. 2 + ... + he N b. N

Waiwai o ka'ōpū mai multiplication i kekahi nuances. Ka huahana o kekahi'ōpū mai i kekahi mea 'ole-commutative, i mea, (he, b) hana i like (he, b).

Ka walaʻauʻana waiwai o matrices nā mea i kekahi mea me ka ana o ka'ē. A ana o ka decorum no ia mau papa ua manaoia e e determinant. Determinant - i kekahi hana o kekahi mau oihana mua o ka huinahalike mua o ka mea n. Ma nā hua'ōlelo, ua kapaia ka determinant determinants. A papaʻaina, me ka lua-mea like, ua like me ka determinant o nā huahana o ka helu a hehee wale o na diagonals elua o ka'ōpū mai A11A22-A12A21. Ke determinant o ka'ōpū mai a hiki i ka mea kiekie oia ka mea determinantsʻia maila kona palaka.

E maopopo pehea lālā mua, Ua hoʻolauna e like ka manaʻo me ka hoouka i ke kaua (koikoi) o ka'ōpū mai. Grade - i ka helu o linearly kuokoa kolamu a me nā lalani o ka papaʻaina. Ka'ōpū mai hiki ke hulu wale ia ka mea, ua piha hoouka i ke kaua, a laila ka hoouka kaua (A) Ua like ke N.

Waiwai o determinants o matrices nā:

1. No ka mea determinant o ka huinahalike'ōpū mai, aole ia e hoʻololi i kona transposition. Ia mea i ka determinant o ka'ōpū mai, e e like me ka determinant o ka papaʻaina i loko o transposed palapala.

2. Inā kekahi kolamu, a me kekahi kaula, e like wale 'Aʻohe hualoaʻa, laila, i ka determinant o ia ka'ōpū mai, e like me' Aʻohe.

3, o ka hoailona o ka determinant o ia i ka papaʻaina, e hoʻololi i ke ku pono Inā i loko o ka'ōpū mai kekahi mau kolamu a me kekahi mau laina interchanged.

4. Ina kekahi kia ao paha kekahi lalani o ka'ōpū mai ua hoonuiia e kekahi helu, laila kona determinant ua hoonuiia e ka ia helu.

5. Ina kekahi hehee ai o ka'ōpū mai ua palapala like me ka huina o elua a oi eiiiiiaiou, ka determinant o keia papaʻaina ua palapala like me ka huina o kekahi mau determinants. Kēlā me kēia determinant o keia dala - keia mea i ka determinant o ka mua, ma i kahi o ka hehee ai na poe ma ka huina, kākau i kekahi o nā hua'ōlelo o ia huina, niioaaonoaaiii, makakoho determinant.

6. Ina kekahi'ōpū mai he mau laina elua o'ālike oihana mua a elua o ka ia kolamu, ke determinant o keia papa, ua like me ke 'Aʻohe.

7. A, i ka determinant mea like i Aʻohe i loko o ia i ka mua, i ka i nā kolamu aiʻelua hoʻi lālani i hapaʻauhau i kekahi i kekahi.

8. Ina e na oihana mua o ka lalani a kia hoonuiia e kekahi helu, a laila, hoʻouka hou aku au ia i nā kumu i loko o ka lalani a kia o ka ia mua, niioaaonoaaiii, laila, i ka determinant o keia papaʻaina e ole loli.

I huina, ua hiki ke olelo aku i ka waiwai o ka'ōpū mai,ʻo ka lākou o ka eiiieaen, akā, i ka mea ia manawa ke kupono ike e pili ana i ke ano o ka makemakika naehana. A pau i ka waiwai o ka'ōpū mai hilinaʻi nui ma luna o kona eiiiiiaiou, a hehee wale.