clopen.solutions

Open problems

1131 registered problems.

OP-00101 Lean verified
The triangle conjecture for the maximal symmetric modulus
FA · OpenProblemsInNLA · spectral order · symmetric moduli · triangle inequalities
OP-00102 Lean verified
Nobori's spectral-middle-factor commutator conjecture
FA · Böttcher–Wenzel inequality · commutators · norm inequalities · OpenProblemsInNLA
OP-00103 Lean verified
A q-permanent inequality for subset-preserving permutations
FA · OpenProblemsInNLA · permanents · q-permanents
OP-00104 Lean verified
Freewan–Hayajneh inequality for sums of weighted geometric means
FA · matrix geometric means · OpenProblemsInNLA · unitarily invariant norms
OP-00105 Lean verified
Lemos–Soares singular-value log-majorization
FA · log-majorization · matrix geometric means · OpenProblemsInNLA · singular values
OP-00106 Lean verified
Corrected generalized geometric-mean product conjecture
FA · eigenvalues · log-majorization · matrix geometric means · OpenProblemsInNLA
OP-00107 Lean verified
Concave unitary-orbit subadditivity without monotonicity
FA · concave functions · matrix subadditivity · OpenProblemsInNLA · unitary orbits
OP-00108 Lean verified
Constant one in the logarithmic commutator inequality
FA · commutators · matrix logarithms · OpenProblemsInNLA
OP-00109 Lean verified
Modulus-order determinant comparison with an arbitrary base power
FA · determinantal inequalities · OpenProblemsInNLA · positive definite matrices
OP-00110 Lean verified
The Rowland–Wu polynomial identity for Sinkhorn limits
NA · matrix scaling · OpenProblemsInNLA · Sinkhorn limits
OP-00111 Lean verified
Full nonnegative rank of the quadratic correlation matrix
NA · extended formulations · nonnegative rank · OpenProblemsInNLA · unique-disjointness matrices
OP-00112 Lean verified
The nonnegative rank of the nine-point distance matrix
NA · Euclidean distance matrices · nonnegative rank · OpenProblemsInNLA
OP-00113 Lean verified
Connectedness of minimal positive semidefinite factorization orbits
NA · matrix factorizations · OpenProblemsInNLA · positive semidefinite rank
OP-00114 Lean verified
Rational factors for rational completely positive boundary matrices
NA · completely positive matrices · OpenProblemsInNLA · rational factorizations
OP-00115 Lean verified
Polynomial trace-error factor after exactly the target rank of pivots
NA · low-rank approximations · OpenProblemsInNLA · pivoted Cholesky factorizations
OP-00116 Lean verified
Improve the randomized LU squared-error factor to 2^k
NA · low-rank approximations · OpenProblemsInNLA · pivoted LU factorizations
OP-00117 Lean verified
Convexity of the expected error of volume-sampled column subsets
NA · column subset selection · elementary symmetric polynomials · OpenProblemsInNLA · volume sampling
OP-00118 Lean verified
Critical-point counts for symmetric rank-two approximation with diagonal zeros
AG · Euclidean distance degrees · low-rank approximations · OpenProblemsInNLA · symmetric matrices
OP-00119 Lean verified
The smallest-multiplier rule for nearest unit-absolute-determinant matrices
NA · Euclidean distance degree · matrix nearness problems · OpenProblemsInNLA
OP-00120 Lean verified
Symmetric minimizer for a positive definite Jordan–Kronecker product
NA · Kronecker products · OpenProblemsInNLA · Rayleigh quotients
OP-00121 Lean verified
A real-valued symbol on a Jordan curve and real Toeplitz spectra
SP · OpenProblemsInNLA · real spectra · Toeplitz matrices
OP-00122 Lean verified
Finitely many unitary classes with prescribed shifted singular values
NA · OpenProblemsInNLA · pseudospectra · unitary similarity
OP-00123 Lean verified
Random column subsets of arbitrary fixed-sparsity matrices
PR · OpenProblemsInNLA · smallest singular values · sparse matrices
OP-00124 Lean verified
Nonnegative H-eigenvalue inheritance from odd-order Hankel tensors
NA · Hankel tensors · H-eigenvalues · OpenProblemsInNLA
OP-00125 Open
Infinite mean condition number in every identifiable tensor format
NA · condition numbers · OpenProblemsInNLA · random tensors · tensor decompositions
OP-00126 Open
Subquadratic overparameterization for iterative decomposition of smoothed tensors
NA · alternating least squares · OpenProblemsInNLA · smoothed analysis · tensor decompositions
OP-00127 Open
Border Comon's conjecture over the complex numbers
AG · border ranks · OpenProblemsInNLA · secant varieties · symmetric tensors
OP-00128 Open
Generic identifiability of tensors at strictly subcritical ranks
AG · identifiability · OpenProblemsInNLA · secant varieties · tensor decompositions
OP-00129 Open
Classification of perfect tensor formats with generic unique decomposition
AG · generic ranks · identifiability · OpenProblemsInNLA · tensor decompositions
OP-00130 Open
Monotonicity of the average number of critical rank-one approximations
NA · critical points · OpenProblemsInNLA · random tensors · rank-one approximations
OP-00131 Open
Exact best-rank-one approximation ratios for general tensor formats
NA · OpenProblemsInNLA · orthogonal tensors · rank-one approximations · spectral norms
OP-00132 Open
Discreteness from below of asymptotic tensor rank
AG · asymptotic ranks · OpenProblemsInNLA · tensor ranks
OP-00133 Open
Irreducibility of asymptotic tensor-rank sublevel varieties
AG · asymptotic ranks · irreducible varieties · OpenProblemsInNLA
OP-00134 Open
Degree-five, six, and nine generation of the Salmon tensor ideal
AG · border ranks · OpenProblemsInNLA · phylogenetic invariants · secant varieties
OP-00135 Open
Cohen–Macaulay coordinate rings for every tensor border-rank variety
AG · Cohen–Macaulay rings · OpenProblemsInNLA · secant varieties · Segre varieties
OP-00136 Open
Entropy formula for the asymptotic subrank of Dicke tensors
CO · asymptotic subranks · Dicke tensors · OpenProblemsInNLA
OP-00137 Partially resolved
Exact partially symmetric rank of products of generalized W tensors
AG · OpenProblemsInNLA · partially symmetric ranks · W-states
OP-00138 Open
Dimension of tensor loci with prescribed minimum border subrank
AG · border subranks · OpenProblemsInNLA · tensor degenerations
OP-00139 Open
The four-exception conjecture for alternating tensor border-rank varieties
AG · alternating tensors · Grassmannians · OpenProblemsInNLA · secant varieties
OP-00140 Partially resolved
Sharp Schatten triangle constants for the arithmetic symmetric modulus
FA · OpenProblemsInNLA · Schatten norms · symmetric moduli · triangle inequalities
OP-00141 Open
Marcus's inequality for the permanent of block permanents
FA · block matrices · OpenProblemsInNLA · permanents
OP-00142 Open
The complex Lu–Wenzel spectral conjecture
FA · Böttcher–Wenzel inequality · commutators · eigenvalue inequalities · OpenProblemsInNLA
OP-00143 Open
The Lih–Wang permanent inequality toward the flat matrix
FA · doubly stochastic matrices · OpenProblemsInNLA · permanents
OP-00144 Partially resolved
Sharp subquadratic Lee constants for sums of matrices
FA · matrix absolute values · norm inequalities · OpenProblemsInNLA · Schatten norms
OP-00145 Partially resolved
Dimension-independent Hlawka constants for Schatten norms
FA · Hlawka-type inequalities · norm inequalities · OpenProblemsInNLA · Schatten norms
OP-00146 Open
Product inequality for disjoint principal minors of Wishart matrices
FA · Gaussian product inequality · OpenProblemsInNLA · principal minors · Wishart matrices
OP-00147 Open
Deterministic regularization of the nonsymmetric eigenproblem
NA · deterministic algorithms · eigenvector condition numbers · OpenProblemsInNLA · pseudospectra
OP-00148 Open
Two permutation matrices generate the doubly stochastic spectral boundary
NA · doubly stochastic matrices · inverse eigenvalue problems · OpenProblemsInNLA · permutation matrices
OP-00149 Partially resolved
A condition number of two for a sign matrix in every dimension
CO · approximate Hadamard matrices · condition numbers · OpenProblemsInNLA · sign matrices
OP-00150 Partially resolved
The optimal decay exponent for the conditioning of sign matrices
CO · approximate Hadamard matrices · condition numbers · OpenProblemsInNLA · sign matrices