The projection onto "Yi" and along all the other "Yj" ( "j" ≠ "i" ) is called the spectral projection of "A" at λ"i" and is usually denoted by "P"(λ"i" ; "A"). Spectral projections are mutually orthogonal in the sense that "P"(λ"i" ; "A") "P"(λ"j" ; "A") = 0 if "i" ≠ "j". Also they commute with "A" and their sum is the identity matrix. Replacing every λ"i" in the Jordan matrix "J" by one and zeroing all other entries gives "P"(λ"i" ; "J"), moreover if "U J U"−1 is the similarity transformation such that "A" = "U J U"−1 then "P"(λ"i" ; "A") = "U P"(λ"i" ; "J") "U"−1. They are not confined to finite dimensions. See below for their application to compact operators, and in holomorphic functional calculus for a more general discussion.