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, iintshukumo zebhola ezenziwa ngexesha lesiqingatha sokuqala zidibanisa kancinci i-zero vector. Ngoko ke zinokungahoywa. Oku kushiya inani eliqingqiweyo lee-rotations \(A_1, ..., A_n \in \mathbb{R}^{3 \times 3}\) kunye ne \(A_k\) orthogonal kunye ne \(\det(A_k) = 1 \,\, \forall \,\, k \in \{1,...,n\}\) . Kuzo naziphi na ii-rotations ezimbini \(A_i, A_j\) oku kulandelayo kuyasebenza::
$$ (A_i A_j)^T (A_i A_j) = A_j^T A_i^T A_i A_j = A_j^T (A_i^T A_i) A_j = A_j^T E_3 A_j = A_j^T A_j = E_3 $$
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.