Lapho umdlalo webhola lezinyawo uqala, ibhola lilele maphakathi nenkundla bese lihanjiswa lizungeze inkundla imizuzu engama-45 ngokushintsha nokujika. Ekuqaleni kwesiwombe sesibili ibhola liphinde libe maphakathi nenkundla. Sikhombisa ngezindlela ezilula ze-algebra eqondile ukuthi inani elingenamkhawulo lamaphuzu ebusweni lihlala lisesimweni esifanayo nasesimweni sokuqala noma ngqo 2.
Okokuqala, ukususwa kwebhola, okwenziwa phakathi nengxenye yokuqala, kuhlanganisa kancane kwi-vector zero. Ngakho-ke banganganakwa. Lokhu kushiya inani elilinganiselwe lokujikeleza \(A_1, ..., A_n \in \mathbb{R}^{3 \times 3}\) nge \(A\) orthogonal kanye \(\det(A_k) = 1 \,\, \forall \,\, k \in \{1,...,n\}\) . \(A_i, A_j\) kuyasebenza:
$$ (A_i A_j)^T (A_i A_j) = A_j^T A_i^T A_i A_j = A_j^T (A_i^T A_i) A_j = A_j^T E_3 A_j = A_j^T A_j = E_3 $$
njengoba
$$ \det(A_i A_j) = \det(A_i) \cdot \det(A_j)=1 \cdot 1 = 1. $$
Lokhu kusho ukuthi \( A_i A_j \) futhi ukujikeleza, yingakho \( A_1 ... A_n \) nakho ukujikeleza okukodwa.
Uma manje \( A_1 ... A_n = E_n \) , kusobala ukuthi wonke amaphuzu obuso bebhola asendaweni yokuqala - kwelinye (okungenzeka) icala i-eigenvector ye \( A_1 ... A_n \) ilingana ne-axis yayo yokujikeleza inani le-eigenvalue \(1\) . Lokhu kusho ukuthi impela lawa maphuzu amabili, asezingeni lokujikeleza, ahlelwe kuwo uqobo.