Idempotent matrices in Julia
Let A be a square matrix of order n . Then A is called an idempotent matrix if AA = A . If a matrix A is idempotent, it follows that A n = A , ∀ n ∈ N . Idempotent matrices behave like identity matrices when raised to a power n . All Idempotent matrices except identity matrices are singular matrices. One way to make idempotent matrices is A = I − u u T , where u is a vector satisfying u T u = 1 . In this case A is symmetric too. #Idempotent matrices in Julia using LinearAlgebra u = rand ( 5 ) u = u / norm ( u ) #Force u^T * u = 1 A = I - u * u ' isapprox ( A ^ 100 , A ) # true isequal ( A , A ' ) # true (test for symmetricity)