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Suppose m, n≥2 are positive integers. Let n be the space of all n×n complex upper triangular matrices, and let ϕ be an injective linear map on m⊗n. Then ϕ(A⊗B) is an idempotent matrix in m⊗n whenever A⊗B is an idempotent matrix in m⊗n if and only if there exists an invertible matrix P∈m⊗n such that ϕ(A⊗B)=P(ξ1(A)⊗ξ2(B))P-1,   ∀A∈m,   B∈n, or when m=n, ϕ(A⊗B)=P(ξ1(B)⊗ξ2(A))P-1,   ∀A∈m,   B∈m, where ξ1([aij])=[aij] or ξ1([aij])=[am-i+1, m-j+1] and ξ2([bij])=[bij] or ξ2([bij])=[bn-i+1, n-j+1]

Linear Maps on Upper Triangular Matrices Spaces Preserving Idempotent Tensor Products