Let G = (V , w) be the associated graph of a non-negative
idempotent matrix of dimension N, where V={1..N}.
Matrix S is shown which is a symmetric and
idempotent matrix as follows:
is an
idempotent matrix with rank r(b - a); we have
Note that the
idempotent matrix AA[degrees] is the projector on R([A.sup.k]) along N([A.sup.k]), where R([A.sup.k]) denotes the range of [A.sup.k] and N([A.sup.k]) is the null space of [A.sup.k].
Beasley,
Idempotent matrix preservers over Boolean algebras, J.
and so the element p[[[gamma].sup.1]] is represented by the
idempotent matrix of order 2p,
If A is cube hermitian then A reduces to an
idempotent matrix.
As in Result 1, though, the null space of the
idempotent matrix I -[[beta].sup.T][([beta]W[[beta].sup.T]).sup.-1][beta]W is spanned by linear combinations of the columns of [[beta].sup.T].
Let B be an n x n symmetric positive semi-definitive matrix and A be an n x n
idempotent matrix of rank r |is less than or equal to~ n; let T be the matrix of the characteristic vectors of A and define