Geodesic
A Matrix Representation of a Pair of Projections in a Hilbert Space
Canadian mathematical bulletin, Tome 14 (1971) no. 1, pp. 35-44

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Let H be a complex Hilbert space and let K = H ⊕ H. Then K can be identified with the set of all column matrices equipped with componentwise addition and scalar multiplication and the scalar product 
Giles, R.; Kummer, H. A Matrix Representation of a Pair of Projections in a Hilbert Space. Canadian mathematical bulletin, Tome 14 (1971) no. 1, pp. 35-44. doi: 10.4153/CMB-1971-006-5
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     author = {Giles, R. and Kummer, H.},
     title = {A {Matrix} {Representation} of a {Pair} of {Projections} in a {Hilbert} {Space}},
     journal = {Canadian mathematical bulletin},
     pages = {35--44},
     year = {1971},
     volume = {14},
     number = {1},
     doi = {10.4153/CMB-1971-006-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-006-5/}
}
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