E.M.S. Hitzer
Imaginary eigenvalues and complex eigenvectors explained by real geometry
Conference Poster: Applied Geometrical Algebras in Computer Science and Engineering, AGACSE 2001,Cambridge, UK.

Abstract: This poster 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 exponentiation. 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 (eigen-)spinors which can be further reduced to underlying vector duplets. The eigenvalues are interpreted as rotation operators, which rotate the underlying vector duplets. The second and third parts of this poster extend and generalize the treatment to three and four dimensions. interpreted as rotation operators, which rotate the underlying vector duplets. The second and third parts of this poster extend and generalize the treatment to three and four dimensions.


[Postscript] 62k, gzip compressed
AGACSE 2001 proceedings paper


[Geometric Calculus Japan index]