MathDB
Problems
Contests
Undergraduate contests
IMC
2000 IMC
3
Complex matrices
Complex matrices
Source: IMC 2000 day 1 problem 3
October 14, 2005
linear algebra
matrix
function
vector
linear algebra unsolved
Problem Statement
Let
A
,
B
∈
C
n
×
n
A,B\in\mathbb{C}^{n\times n}
A
,
B
∈
C
n
×
n
with
ρ
(
A
B
−
B
A
)
=
1
\rho(AB - BA) = 1
ρ
(
A
B
−
B
A
)
=
1
. Show that
(
A
B
−
B
A
)
2
=
0
(AB - BA)^2 = 0
(
A
B
−
B
A
)
2
=
0
.
Back to Problems
View on AoPS