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- W2960185655 abstract "Schoenberg showed that a function $f:(-1,1)rightarrow mathbb{R}$ such that $C=[c_{ij}]_{i,j}$ positive semi-definite implies that $f(C)=[f(c_{ij})]_{i,j}$ is also positive semi-definite must be analytic and have Taylor series coefficients nonnegative at the origin. The Schoenberg theorem is essentially a theorem about the functional calculus arising from the Schur product, the entrywise product of matrices. Two important properties of the Schur product are that the product of two rank one matrices is rank one, and the product of two positive semi-definite matrices is positive semi-definite. We classify all products which satisfy these two properties and show that these generalized Schur products satisfy a Schoenberg type theorem." @default.
- W2960185655 created "2019-07-23" @default.
- W2960185655 creator A5005813786 @default.
- W2960185655 date "2019-07-10" @default.
- W2960185655 modified "2023-09-27" @default.
- W2960185655 title "Noncommutative Schur-type products and their Schoenberg theorem" @default.
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