# idempotent matrix

## idempotent matrix

[¦i‚dem¦pōt·ənt ′mā·triks]
(mathematics)
A matrix E satisfying the equation E 2= E.
References in periodicals archive ?
Let G = (V , w) be the associated graph of a non-negative idempotent matrix of dimension N, where V={1..N}.
In 2017, we showed that a maximal subgroup of the multiplicative semigroup of n x n tropical matrices containing a nonsingular idempotent matrix E is isomorphic to the group of all invertible matrices which commute with E as groups and proved that each maximal subgroup of the multiplicative semigroup of n x n tropical matrices with the identity of the rank r is isomorphic to some maximal subgroup of the multiplicative semigroup of r x r tropical matrices with nonsingular identity.
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].
is an n x n symmetric idempotent matrix with rank n - p in which the prime denotes the matrix transposition and [(X'X).sup.-] is a generalized inverse of X'X.
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
Note that the idempotent matrix A[A.sup.D] is the projector on R([A.sup.k]) alongside N([A.sup.k]), whereas R([A.sup.k]) denotes the range of [A.sup.k] and N([A.sup.k]) is the null space of [A.sup.k].
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