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- W2049205715 abstract "We characterize ordered orthonormal bases ${s_1,dots,s_n} subset mathbb{R}^n$ for which the matrix $s_1s_1^T+dots+s_ts_t^T$ is nonnegative for each $t=1,dots,n$. In particular we show that the associated orthogonal matrix $S=[s_1,s_2,dots,s_n]$ has certain submatrices that are Soules matrices. Based on the construction of Soules bases developed by Elsner, Nabben, and Neumann [Linear Algebra Appl., 271 (1998), pp. 323–343] we are able to construct all possible such bases. Additionally, we show that this set is the closure of the set of Soules bases. We also include some results regarding matrix functions of $S Lambda S^T$, where $Lambda$ is a diagonal matrix with nonincreasing diagonal entries." @default.
- W2049205715 created "2016-06-24" @default.
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- W2049205715 date "2010-01-01" @default.
- W2049205715 modified "2023-09-25" @default.
- W2049205715 title "On a Generalization of Soules Bases" @default.
- W2049205715 doi "https://doi.org/10.1137/080732407" @default.
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