Geometriae Dedicata

, Volume 63, Issue 2, pp 113–121 | Cite as

Angles between Euclidean subspaces

  • Sheng Jiang


The angle between two subspaces of dimensions p and q in a Euclidean space is considered by using exterior algebra. Some properties of angles are obtained. The relation between such a higher dimensional angle and the usual principal angles is also given. And finally, an application to Grassmann manifolds is briefly discussed.

Mathematics Subject Classifications (1991)

51M05 51M16 51K05 

Key words

higher-dimensional angle principal angles Grassmann manifolds 


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  1. 1.
    Dörband, W.: Determinantensätze und Simplexeigenschaften, Math. Nachr. 44 (1970), 295–304.Google Scholar
  2. 2.
    Eriksson, F.: The law of sines for tetrahedra and n-simplices, Geom. Dedicata 7 (1978), 71–80.Google Scholar
  3. 3.
    Lin, S.-Y. T. and Lin, Y.-F.: The n-dimensional Pythagorean theorem, Linear Multilinear Algebra 26 (1990), 9–13.Google Scholar
  4. 4.
    Miao, J. and Ben-Israel, A.: On principal angles between subspaces in R n, Linear Algebra Appl. 171 (1992), 81–98.Google Scholar
  5. 5.
    Hotelling, H.: Relations between two sets of variates, Biometrica 28 (1936), 321–377.Google Scholar
  6. 6.
    Bourbaki, N.: Algèbre, Hermann, Paris, 1948.Google Scholar
  7. 7.
    Flanders, H.: Differential Forms, Academic Press, New York, London, 1963.Google Scholar
  8. 8.
    Blumenthal, L. M.: Theory and Applications of Distance Geometry, Chelsea Pub. Co., New York, 1970.Google Scholar
  9. 9.
    Chen, W. H.: The differential geometry of Grassmann manifolds as submanifolds (in Chinese), Acta Math. Sinica 31 (1988), 46–53. (MR 89h: 53116.)Google Scholar
  10. 10.
    Jiang, S.: Identities of Laplace type and decomposable m-vectors, Math. Practice Theory (in Chinese), 1 (1993), 82–85. (MR 94d: 53026.)Google Scholar
  11. 11.
    Cartan, E.: Les systèmes différentiels extérieurs et leurs applications géometriques, Paris, 1945.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Sheng Jiang
    • 1
  1. 1.Department of MathematicsYangzhou UniversityYangzhouP.R. China

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