Positivity preservers forbidden to operate on diagonal blocks
نویسندگان
چکیده
منابع مشابه
A Note on Positivity Preservers
In this short follow-up of [3] we answer some questions posed there. In particular, we characterize two natural classes of linear operators acting on R[x1, x2, ..., xn] which (i) preserve the set of positive n-variate polynomials; (ii) either act diagonally in the monomial basis of R[x1, x2, ..., xn] or are translation-invariant.
متن کاملRepresentation and Approximation of Positivity Preservers
We consider a closed set S ⊆ Rn and a linear operator Φ: R[X1, . . . , Xn]→ R[X1, . . . , Xn] that preserves nonnegative polynomials, in the following sense: if f ≥ 0 on S, then Φ(f) ≥ 0 on S as well. We show that each such operator is given by integration with respect to a measure taking nonnegative functions as its values. This can be seen as a generalization of Haviland’s Theorem, which conc...
متن کاملMatrix positivity preservers in fixed dimension
A celebrated 1942 result of Schoenberg characterizes all entry-wise functions which preserve positivity of matrices of any size. I will present a characterization of polynomials which preserve positivity when applied entry-wise on matrices of a fixed dimension. All put in historical context and motivated by recent demands of statistics of large data and optimization theory. A sketch of the proo...
متن کاملPositivity of the Diagonal
We study how the geometry of a projective variety X is reflected in the positivity properties of the diagonal ∆X considered as a cycle on X ×X. We analyze when the diagonal is big, when it is nef, and when it is rigid. In each case, we give several implications for the geometric properties of X. For example, when the cohomology class of ∆X is big, we prove that the Hodge groups H(X) vanish for ...
متن کاملReordering Diagonal Blocks in Real Schur Form
We present a direct algorithm for computing an orthogonal similarity transformation which interchanges neighboring diagonal blocks in a matrix in real Schur form. The algorithm does not require the solution of the associated Sylvester equation. Numerical tests suggest the backward stability of the scheme.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2020
ISSN: 1088-6850,0002-9947
DOI: 10.1090/tran/8256