is an n x n symmetric idempotent matrix with rank n - p in which the prime denotes the matrix transposition and [(X'X).
R] is a symmetric idempotent matrix of rank k, Q is the symmetric rank (n - p) idempotent matrix given in equation (3), and [Q.
n-p] is an n x (n - p) matrix containing the eigenvectors of the unit eigenvalues of the symmetric idempotent matrix Q, such that
Beasley, Idempotent matrix
preservers over Boolean algebras, J.
1]] is represented by the idempotent matrix of order 2p,
If we apply this retraction map to our idempotent matrix [[gamma].
Given a smooth complex vector bundle [xi], represented by an idempotent matrix [phi] of order n, over the ring of smooth functions on the base, the Chern classes of [xi] in the standard de Rham cohomology of differential forms, are given as follows:
If A is cube hermitian then A reduces to an idempotent matrix
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
Thus, since A is an idempotent matrix, then by Theorem 1, we need only show that