Let
P
P
and
Q
Q
be two idempotents on a Hilbert space. In this note, we prove that the invertibility of the linear combination
λ
1
P
+
λ
2
Q
\lambda _1P+\lambda _2Q
is independent of the choice of
λ
i
\lambda _i
,
i
=
1
,
2
,
i=1,2,
if
λ
1
λ
2
≠
0
\lambda _1\lambda _2\neq 0
and
λ
1
+
λ
2
≠
0.
\lambda _1+\lambda _2\neq 0.