Nā lālani pili laina a kūʻokoʻa: wehewehe, nā laʻana

Ma kēia hoʻolaha, e noʻonoʻo mākou i ke ʻano o ka hui pū ʻana o nā kaula, laina laina a me nā kaula kūʻokoʻa. E hāʻawi pū mākou i nā laʻana no ka hoʻomaopopo maikaʻi ʻana i ka mea theoretical.

Ka wehewehe ʻana i kahi hui laina laina o nā kaula

Hui laina laina (LK) manawa s₁me₂, …, s_n Ke kumu A kapa ʻia he ʻōlelo o kēia ʻano:

Fins₁ + αs₂ + … + αs_n

Inā pau nā coefficients α_i ua like me ka ale, pela LC kūleʻaʻole. Ma nā huaʻōlelo ʻē aʻe, ua like ka hui laina trivial i ka lālani zero.

ʻo kahi laʻana: 0 · s₁ + 0 · s₂ + 0 · s₃

No laila, inā he hoʻokahi o nā coefficients α_i 'a'ole like me ka 'ole, a laila 'o LC mea ole.

ʻo kahi laʻana: 0 · s₁ + 2 · s₂ + 0 · s₃

Nā lālani pili laina a kūʻokoʻa

ʻO ka ʻōnaehana kaula pili laina (LZ) inā loaʻa kahi hui laina ʻole-trivial o lākou, ua like ia me ka laina ʻole.

No laila, hiki i ka LC non-trivial i kekahi mau hihia ke like me ke kaula zero.

ʻO ka ʻōnaehana kaula kūʻokoʻa laina laina (LNZ) inā like ka LC liʻiliʻi me ke kaula null.

Notes:

• I loko o kahi matrix square, ʻo ka ʻōnaehana lālani he LZ wale nō inā ʻo ka mea hoʻoholo o kēia matrix he zero (ka = 0).
• I loko o kahi matrix square, ʻo ka ʻōnaehana lālani he LIS wale nō inā ʻaʻole like ka mea hoʻoholo o kēia matrix me ka ʻole (ka ≠ 0).

Laʻana o kahi pilikia

E ʻike kākou inā ʻo ka ʻōnaehana string {s₁ = {3 4};s₂ = {9 12}} pili laina.

Hoʻoholo:

1. ʻO ka mua, e hana kākou i LC.

α₁{3 4} + a₂{9 12}.

2. I kēia manawa e ʻike kākou i nā waiwai e pono ai ke lawe α₁ и α₂i like ka hui laina me ke kaula null.

α₁{3 4} + a₂{9 12} = {0 0}.

3. E hana kākou i ʻōnaehana o nā hoohalike:

4. E puunaue i ka hoohalike mua me ekolu, o ka lua me na eha.

5. ʻO ka hoʻonā o kēia ʻōnaehana kekahi α₁ и α₂, Me ka α₁ = -3a₂.

ʻO kahi laʻana, inā α₂ = 2alaila, α₁ =-6. Hoʻololi mākou i kēia mau waiwai i loko o ka ʻōnaehana o nā hoʻohālikelike ma luna a loaʻa:

pane mai: pela na laina s₁ и s₂ pili laina.