Drazin inverse

• If A is invertible with inverse, then.
• The Drazin inverse of a matrix of index 0 or 1 is called the group inverse or -inverse and denoted A^#. The group inverse can be defined, equivalently, by the properties AA^#A = A, A^#AA^# = A^#, and AA^# = A^#A.
• A projection matrix P, defined as a matrix such that P² = P, has index 1 and has Drazin inverse P^D = P.
• If A is a nilpotent matrix, then