Definition. Let be a vector space. A linear involution is a linear operator such that is the identity operator on . An equivalent definition is that a linear involution is a linear operator that equals its own inverse.
Theorem 2. Let and be linear operators on a
vector space over a field of characteristic not 2, and let be the identity operator on .
If is an involution then
are projection operators.
Conversely, if is a projection operator, then
the operators are involutions.
Involutions have important application in expressing hermitian-orthogonal operators, that is, . In fact, it may be represented as
|Date of creation||2013-03-22 13:34:37|
|Last modified on||2013-03-22 13:34:37|
|Last modified by||matte (1858)|