Abstract
In this paper the basic results on angles between subspaces of Cn are presented in a way that differs from the abstract mathematical narrative of Kato [10] et al. First the intuitively clear properties of the angle between one dimensional subspaces of R2 are stated using orthogonal projections. Then, using the singular value decomposition, a very simple representation is derived for pairs of orthogonal projections in Cn. Through this representation the angles between two subspaces of Cn are related to the principal angles between certain invariant two dimensional subspaces. It is seen how the properties of angles between general subspaces can be derived from the corresponding simple properties of angles between two dimensional subspaces. The results are used to estimate angles between certain subspaces. These estimates are not new. But the point made here is that when the relevant perturbation identities are known it is easy to use an angle function to get perturbation bounds. Finally in appendix 1 a new perturbation bound is given for pairs of oblique projections.
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Wedin, P.Å. (1983). On angles between subspaces of a finite dimensional inner product space. In: Kågström, B., Ruhe, A. (eds) Matrix Pencils. Lecture Notes in Mathematics, vol 973. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062107
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DOI: https://doi.org/10.1007/BFb0062107
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