In this thesis we study projectors in a complex space and the principal angles between subspaces together with the corresponding principal vectors, as well as their properties and mutual relationships. The Halmos and Wedin theorems play a key role, as they provide a canonical decomposition of a pair of projectors with respect to the principal angles. Using this decomposition, we analyze the properties of the sum, difference, and product of two projectors. We also consider the question of when a given Hermitian matrix can be expressed as the sum or difference of two projectors. For the product, it turns out that the singular values of the product are closely related to the principal angles.
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