MathDB
Problems
Contests
National and Regional Contests
Korea Contests
South Korea USCM
2018 Korea USCM
5
5
Part of
2018 Korea USCM
Problems
(1)
Range of spectral radius
Source: 2018 South Korea USCM P5
8/14/2020
A real symmetric
2018
×
2018
2018\times 2018
2018
×
2018
matrix
A
=
(
a
i
j
)
A=(a_{ij})
A
=
(
a
ij
)
satisfies
∣
a
i
j
−
2018
∣
≤
1
|a_{ij}-2018|\leq 1
∣
a
ij
−
2018∣
≤
1
for every
1
≤
i
,
j
≤
2018
1\leq i,j\leq 2018
1
≤
i
,
j
≤
2018
. Denote the largest eigenvalue of
A
A
A
by
λ
(
A
)
\lambda(A)
λ
(
A
)
. Find maximum and minumum value of
λ
(
A
)
\lambda(A)
λ
(
A
)
.
linear algebra
matrix
spectrum
college contests