# Ibhola ekhatywayo kunye neNgcaciso yeAlgebra0417

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