Let
(1)
|
and
(2)
|
Then there exists an Hermitian matrix with eigenvalues and diagonal elements iff
(3)
|
for all and with equality for . The theorem is sometimes also known as Schur's theorem.
Let
(1)
|
and
(2)
|
Then there exists an Hermitian matrix with eigenvalues and diagonal elements iff
(3)
|
for all and with equality for . The theorem is sometimes also known as Schur's theorem.
This entry contributed by Fred Manby
Manby, Fred. "Horn's Theorem." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/HornsTheorem.html