4 problems

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Uniqueness of sum-of-squares decompositions up to orthogonal equivalence
Let $f\in \operatorname{Sym}^{2d}V$ be generic of SOS-rank $k\leq n$ , and let … For a decomposition of $f$ into $k$ squares, write $A\in\mathbb C^k\otimes\mathbb C^N$ for the coeff…
Conjectureopenalgebraic-geometry gram-matrices sums-of-squaresarXiv posted 2 days ago
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Cross Gramian coherence lower-bound conjecture for dual frames
Let $F$ be a frame for $\mathbb{F}^n$ , and let $G$ be one of its dual frames. Write $Gr(F,G)$ for their cross Gramian and let $\mu(Gr(F,G))$ denote its maximum off-diagonal magnitu…
Conjectureopencoherence frame-theory gram-matricesarXiv posted 2 days ago
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Inverse-eigenvector product conjecture for Gram matrices
Inverse-eigenvector product conjecture. There exists an inverse eigenvector $\alpha$ such that
Conjectureopengram-matrices linear-algebra polarization-constantsarXiv posted 2 days ago
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Gram-matrix parity conjecture for the dual canonical basis
Gram-matrix parity conjecture. One has
Conjectureopengram-matrices non-hermitian-quantum-systems temperley-lieb-algebrasarXiv posted 2 days ago

Uniqueness of sum-of-squares decompositions up to orthogonal equivalence