ヒッツェル,エクハルト   HITZER, Eckhard
  ヒッツェル, エクハルト
   所属   国際基督教大学教養学部 アーツ・サイエンス学科
   職種   上級准教授
言語種別 英語
発行・発表の年月 2001
形態種別 研究論文(国際会議プロシーディングス)
査読 査読あり
標題 Imaginary eigenvalues and complex eigenvectors explained by real geometry
執筆形態 単著
掲載誌名 Applied Geometrical Algebras in Computer Science and Engineering, AGACSE 2001, Birkhauser
掲載区分国外
出版社・発行元 Birkhaeuser, Basel, Switzerland.
巻・号・頁 pp.145-153
著者・共著者 HITZER Eckhard
概要 This paper first reviews how anti-symmetric matrices in two dimensions yield imaginary eigenvalues and complex eigenvectors. It is shown how this carries on to rotations by means of the Cayley transformation. Then a real geometric interpretation is given to the eigenvalues and eigenvectors by means of real geometric algebra. The eigenvectors are seen to be two component eigenspinors which can be further reduced to underlying vector duplets. The eigenvalues are interpreted as rotation operators, which rotate the underlying vector duplets. The second part of this paper extends and generalizes the treatment to three dimensions. Finally the four-dimensional problem is stated.