  Principal angles between subspaces (PABS) (also called canonical angles)
serve as a classical tool in mathematics, statistics, and applications, e.g.,
data mining. Traditionally, PABS are introduced via their cosines. The cosines
and sines of PABS are commonly defined using the singular value decomposition.
We utilize the same idea for the tangents, i.e., explicitly construct matrices,
such that their singular values are equal to the tangents of PABS, using
several approaches: orthonormal and non-orthonormal bases for subspaces, as
well as projectors. Such a construction has applications, e.g., in analysis of
convergence of subspace iterations for eigenvalue problems.
