Introduces structured matrix factorization length and X-factorization varieties, computes their dimensions for Toeplitz, Hankel, bidiagonal, tridiagonal, skew-symmetric, and companion matrices, and proposes displacement-rank lower bounds and alternating-minimization upper bounds.
STRUCTURED MATRIX FACTORIZATION LENGTH 33
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Derives combinatorial expression for degrees of tensor train varieties via integral geometry and releases Julia package TTVarietyDegree.jl.
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Structured matrix factorization length
Introduces structured matrix factorization length and X-factorization varieties, computes their dimensions for Toeplitz, Hankel, bidiagonal, tridiagonal, skew-symmetric, and companion matrices, and proposes displacement-rank lower bounds and alternating-minimization upper bounds.
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Degree of tensor train varieties via integral geometry
Derives combinatorial expression for degrees of tensor train varieties via integral geometry and releases Julia package TTVarietyDegree.jl.