Contents
Ma kēia hoʻolaha, e noʻonoʻo mākou i ka wehewehe ʻana o ke kūlana o kahi matrix, a me nā ʻano e hiki ai ke loaʻa. E kālailai pū mākou i nā laʻana e hōʻike i ka hoʻohana ʻana o ke kumumanaʻo i ka hana.
Ka hoʻoholo ʻana i ke kūlana o kahi matrix
Kūlana matrix ʻo ia ke kūlana o kona ʻōnaehana o nā lālani a i ʻole nā kolamu. Loaʻa i kēlā me kēia matrix kona lālani a me ke kolamu, ua like kekahi me kekahi.
Kūlana ʻōnaehana lālani ʻo ia ka helu kiʻekiʻe o nā lālani kūʻokoʻa laina. Hoʻoholo ʻia ke kūlana o ka ʻōnaehana kolamu ma ke ʻano like.
Notes:
- ʻO ke kūlana o ka matrix zero (i hōʻike ʻia e ka hōʻailona “θ“) o kēlā me kēia nui he zero.
- ʻO ke kūlana o kēlā me kēia kaha lālani nonzero a i ʻole vector kolamu ua like ia me hoʻokahi.
- Inā loaʻa i ka matrix o kekahi nui ma lalo o hoʻokahi mea i like ʻole me ka zero, a laila ʻaʻole emi kona kūlana ma mua o hoʻokahi.
- ʻAʻole ʻoi aku ka nui o ka matrix ma mua o kona ana liʻiliʻi.
- ʻAʻole hoʻololi ka hoʻololi haʻahaʻa i hana ʻia ma kahi matrix i kona kūlana.
Ke ʻimi nei i ke kūlana o kahi matrix
ʻO ke ala liʻiliʻi
ʻO ke kūlana o kahi matrix ua like ia me ka ʻoi loa o ka helu ʻole.
Penei ka algorithm: e imi i na kamalii mai ka papa haahaa a hiki i ke kiekie. Inā ʻuʻuku nʻAʻole like ke kauoha me ka ʻole, a ʻo nā mea a pau ma hope (n+1) ua like me 0, no laila, ʻo ke kūlana o ka matrix n.
la'ana
No ka hoʻomaʻamaʻa ʻana, e lawe kākou i kahi laʻana kūpono a ʻimi i ke kūlana o ka matrix A ma lalo, e hoʻohana ana i ke ʻano o ka palena ʻana i nā keiki liʻiliʻi.
pāʻoihana
Ke hana nei mākou i kahi matrix 4 × 4, no laila, ʻaʻole hiki ke kiʻekiʻe kona kūlana ma mua o 4. Eia kekahi, aia nā mea ʻole-zero i loko o ka matrix, ʻo ia hoʻi ʻaʻole i emi kona kūlana ma mua o hoʻokahi. No laila e hoʻomaka kākou:
1. Hoʻomaka e nānā nā keiki o ka papa ʻelua. No ka hoʻomaka ʻana, lawe mākou i ʻelua lālani o nā kolamu mua a me ka lua.
Ua like ka liʻiliʻi me ka ʻole.
No laila, neʻe mākou i ka mea liʻiliʻi aʻe (e mau ana ke kolamu mua, a ma kahi o ka lua e lawe mākou i ke kolu).
ʻO ka mea liʻiliʻi he 54≠0, no laila ʻo ke kūlana o ka matrix ma kahi o ʻelua.
'Ōlelo Aʻo: Inā ua like kēia keiki liʻiliʻi me ka ʻole, e nānā hou mākou i kēia mau hui pū ʻana:
Inā makemake ʻia, hiki ke hoʻomau ʻia ka helu ʻana ma ke ʻano like me nā kaula:
- 1 a me 3;
- 1 a me 4;
- 2 a me 3;
- 2 a me 4;
- 3 a me 4.
Inā like nā keiki liʻiliʻi o ka papa ʻelua me ka ʻole, a laila ua like ka pae o ka matrix i hoʻokahi.
2. Aneane hiki koke iā mākou ke ʻimi i kahi keiki ʻuʻuku i kūpono iā mākou. No laila e neʻe kākou i ka nā keiki o ke kolu o ke kauoha.
I ka mea liʻiliʻi i loaʻa o ka papa ʻelua, ka mea i hāʻawi i kahi hopena ʻole, hoʻohui mākou i hoʻokahi lālani a me kekahi o nā kolamu i hōʻike ʻia i ka ʻōmaʻomaʻo (hoʻomaka mākou mai ka lua).
Ua lilo ka mea ʻuʻuku i ka ʻole.
No laila, hoʻololi mākou i ke kolamu ʻelua i ka hā. A i ka lua o ka ho'āʻo ʻana, hiki iā mākou ke ʻimi i kahi mea liʻiliʻi ʻaʻole like me ka zero, ʻo ia hoʻi ʻaʻole hiki ke emi ka pae o ka matrix ma mua o 3.
'Ōlelo Aʻo: inā i lilo ka hopena i zero hou, ma kahi o ka lālani ʻelua, e lawe hou mākou i ka ʻehā a hoʻomau i ka ʻimi ʻana i kahi keiki "maikaʻi".
3. I kēia manawa ke hoʻoholo nei nā keiki o ka papa ʻehā ma muli o ka mea i ʻike mua ʻia. I kēia hihia, ʻo ia ka mea e pili ana i ka mea hoʻoholo o ka matrix.
Ua like ka liʻiliʻi me 144≠0. 'O ia ho'i ke kūlana o ka matrix A like 4.
Hoʻemi ʻia o kahi matrix i kahi ʻano stepped
ʻO ke kūlana o kahi matrix step e like me ka helu o kāna mau lālani non-zero. ʻO ia, ʻo nā mea a pau e pono ai mākou e lawe i ka matrix i ke ʻano kūpono, no ka laʻana, me ka hoʻohana ʻana, e like me kā mākou i ʻōlelo ai ma luna, mai hoʻololi i kona kūlana.
la'ana
E huli i ke kūlana o ka matrix B malalo. ʻAʻole mākou e lawe i kahi hiʻohiʻona paʻakikī, no ka mea, ʻo kā mākou pahuhopu nui wale nō ka hōʻike ʻana i ka hoʻohana ʻana o ke ʻano i ka hana.
pāʻoihana
1. ʻO ka mua, e unuhi i ka papalua mua mai ka laina ʻelua.
2. Ano, e unuhi i ka lalani mua mai ka lalani ekolu, i hoonuiia me eha.
No laila, ua loaʻa iā mākou kahi matrix ʻanuʻu i like ka helu o nā lālani ʻaʻole ʻelua me ʻelua, no laila ua like kona kūlana me 2.