Ibhola ekhatywayo kunye neNgcaciso yeAlgebra

Xa umdlalo webhola uqala, ibhola ilele embindini webala kwaye emva koko ishukunyiswe ijikeleze ibala kangangemizuzu engama-45 ngokutshintsha nokujika. Ekuqaleni kwesiqingatha sesibini, ibhola iphinda iphinde ibekho embindini webala. Sibonisa ngeendlela ezilula ze-algebra emgceni yokuba inani elingenasiphelo lamanqaku kumphezulu lihlala likwindawo enye nasebusweni bokuqala okanye ngokuchanekileyo 2.


Okokuqala, ukufuduswa kwebhola okwenziwa ngexesha lesiqingatha sokuqala kudibanisa i-zero vector, kancinci. Banako ke ukungahoywa. Oku kushiya inani eligqityiweyo lokujikeleza \(A_1, ..., A_n \in \mathbb{R}^{3 \times 3}\) nge \(A\) orthogonal kunye \(\det(A_k) = 1 \,\, \forall \,\, k \in \{1,...,n\}\) . Yonke \(A_i, A_j\) emibini \(A_i, A_j\) iyasebenza:

$$ (A_i A_j)^T  (A_i A_j) = A_j^T   A_i^T   A_i   A_j = A_j^T (A_i^T   A_i)   A_j = A_j^T   E_3   A_j = A_j^T   A_j = E_3 $$

njenge

$$ \det(A_i A_j) = \det(A_i) \cdot \det(A_j)=1 \cdot 1 = 1. $$

Oku kuthetha ukuba \( A_i A_j \) kwakhona ujikelezo, yiyo loo nto \( A_1 ... A_n \) olunye.

Ukuba ngoku \( A_1 ... A_n = E_n \) , ngokucacileyo onke amanqaku obuso bebhola ngqo kwindawo yokuqala-kwelinye icala (elinokwenzeka) imeko ye-eigenvector ye \( A_1 ... A_n \) ilingana ne-axis yayo yokujikeleza ixabiso le-eigenvalue \(1\) . Oku kuthetha ukuba kanye la manqaku mabini, alele kwi-axis yokujikeleza, azotywe kuwo.

Emva