 Sometimes spectral projections inherit properties from their parent operators.For example if "T" is a positive matrix with spectral radius "r" then the Perron–Frobenius theorem asserts that "r" ∈ "σ"("T").The associated spectral projection "P" = "P"("r";"T") is also positive and by mutual orthogonality no other spectral projection can have a positive row or column.