线性变换题设α,β是线性变换,且α^2=α,β^2=β,如果（α+β）^2=α+β,则αβ=0.

Question

线性变换题
设α,β是线性变换,且α^2=α,β^2=β,如果（α+β）^2=α+β,则αβ=0 .

Answer 1

（α+β）^2 = α^2 + β^2 + 2αβ = α + β + 2αβ （α+β）^2 = α+β α + β + 2αβ = α+β 2αβ = 0; αβ=0;