In mathematics, the determinantal conjecture of Marcus (1972) and de Oliveira (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.
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In mathematics, the determinantalconjecture of Marcus (1972) and de Oliveira (1982) asks whether the determinant of a sum A + B of two n by n normal...
A {\displaystyle A} . Determinantalconjecture on the determinant of the sum of two normal matrices. Eilenberg–Ganea conjecture: a group with cohomological...
itself has Jacobian determinant which is a non-zero constant, then the function has a polynomial inverse. It was first conjectured in 1939 by Ott-Heinrich...
the Jacobian determinant is nonzero at x (see Jacobian conjecture for a related problem of global invertibility). The Jacobian determinant also appears...
Bourque & Ligh (1992) conjectured that the LCM matrix on a GCD-closed set S {\displaystyle S} is nonsingular. This conjecture was shown to be false by...
p-adic determinant method. The main use of Heath-Brown's determinant method has been to try to solve the so-called dimension growth conjecture. Aside...
In mathematics, the Frobenius determinant theorem was a conjecture made in 1896 by the mathematician Richard Dedekind, who wrote a letter to F. G. Frobenius...
In mathematics, the Weil conjectures were highly influential proposals by André Weil (1949). They led to a successful multi-decade program to prove them...
In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers...
Specifically, the Hadamard conjecture proposes that a Hadamard matrix of order 4k exists for every positive integer k. The Hadamard conjecture has also been attributed...
In probability theory, the KPZ fixed point is a markov field and conjectured to be a universal limit of a wide range of stochastic models forming the...
Mertens conjecture was proven false in 1985 by Andrew Odlyzko and Herman te Riele. However, the Riemann hypothesis is equivalent to a weaker conjecture on...
effects into general relativity seem to show that the chronology protection conjecture postulated by physicist Stephen Hawking fails to prevent the formation...
octagon is a region in the plane found by Karl Reinhardt in 1934 and conjectured by him to have the lowest maximum packing density of the plane of all...
complex Grassmannians. This was one of the clues leading to the Weil conjectures. Note that in the limit q ↦ 1 the order of GL(n, q) goes to 0! – but...
some of these conjectures implying fast matrix multiplication are incompatible with another plausible conjecture, the sunflower conjecture, which in turn...
for appropriately defined spatial scale factors. This is called the BKL conjecture. For most types of matter the effect of the matter fields on the dynamics...
The matrix of intersection numbers of a basis of the two-cycles is conjectured to be the Cartan matrix of the Lie algebra of this local symmetry group...
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