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Abstract Consider a pair of elementsfandgin a commutative ringQ. Given a matrix factorization offand another ofg, the tensor product of matrix factorizations, which was first introduced by Knörrer and later generalized by Yoshino, produces a matrix factorization of the sum$$f+g$$. We will study the tensor product ofd-fold matrix factorizations, with a particular emphasis on understanding when the construction has a non-trivial direct sum decomposition. As an application of our results, we construct indecomposable maximal Cohen–Macaulay and Ulrich modules over hypersurface domains of a certain form.
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This content will become publicly available on March 26, 2026
On the optimal arrangement of 2 d lines in ℂ d
Abstract We show the optimal coherence of $2d$ lines in $$\mathbb{C}^{d}$$ is given by the Welch bound whenever a skew Hadamard matrix of order $d+1$ exists. Our proof uses a variant of Hadamard matrix doubling that converts any equiangular tight frame of size $$\tfrac{d-1}{2} \times d$$ into another one of size $$d \times 2d$$. Among $$d \leq 160$$, this produces equiangular tight frames of new sizes when $d = 11$, $35$, $39$, $43$, $47$, $59$, $67$, $71$, $83$, $95$, $103$, $107$, $111$, $119$, $123$, $127$, $131$, $143$, $151$ and $155$.
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- Award ID(s):
- 2220301
- PAR ID:
- 10585691
- Publisher / Repository:
- arXiv:2312.09975
- Date Published:
- Journal Name:
- Information and Inference: A Journal of the IMA
- Volume:
- 14
- Issue:
- 2
- ISSN:
- 2049-8772
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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