Determinantal conjecture
{{Short description|Mathematical conjecture}}
In mathematics, the determinantal conjecture of {{harvs|txt|last=Marcus|year=1972}} and {{harvs|txt|last=de Oliveira|year=1982}} asks whether the determinant of a sum A + B of two n by n normal complex matrices A and B lies in the convex hull of the n! points Πi (λ(A)i + λ(B)σ(i)), where the numbers λ(A)i and λ(B)i are the eigenvalues of A and B, and σ is an element of the symmetric group Sn.
References
- {{Citation | last1=de Oliveira | first1=G.N. | title=Research problem: Normal matrices | year=1982 | journal=Linear and Multilinear Algebra | volume=12 | pages=153–154| doi=10.1080/03081087.1982.11882087 }}
- {{Citation | last1=Marcus | first1=Marvin | title=Derivations, Plücker relations, and the numerical range | mr=0314862 | year=1972 | journal=Indiana University Mathematics Journal | issn=0022-2518 | volume=22 | issue=12 | pages=1137–1149| doi=10.1512/iumj.1973.22.22094 }}
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