In mathematics, the determinantal conjecture of and asks whether the

determinant In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if and ...

of a sum ''A'' + ''B'' of two ''n'' by ''n'' normal complex matrices ''A'' and ''B'' lies in the

convex hull In geometry, the convex hull or convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space ...

of the ''n''! points Π_''i'' (''λ(A)''_''i'' + ''λ(B)''_σ(''i'')), where the numbers ''λ(A)''_''i'' and ''λ(B)''_''i'' are the

eigenvalues In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted b ...

of ''A'' and ''B'', and ''σ'' is an element of the symmetric group ''S''_''n''.

References

* * Determinants Conjectures {{algebra-stub