摘要
本文继续前文(Ⅰ)的讨论,主要讨论加强p除环上自共轭阵与正定自共轭阵酉相似于对角阵的理论及其各种应用。由于实四元环是一个加强p除环,故本文一切结论对实四元数除环上的方阵自然也正确。
This is a continuation of the previous paper ( 1 ) . In this paper , a use ful basic theorem that every selfconjugate matrix over the strong p division ring Ω is unitary similar to a tridiagorial matrix over the conter o f Ω is gi ven thus all of famous results involving selfconjugate matrices, positivedefinite selfcon jugate matrices, nonnegative selfconjugate matrix in the ordiniry com plex matrix theory are generalized to selfconjugate matrices over Ω . and S1 gular decomuposition as well as polar decomposition in the ordinary compl ex matrix theory are also generalized to matrices over Ω .
