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REPORTS > AUTHORS > ANAND KUMAR NARAYANAN:
All reports by Author Anand Kumar Narayanan:

TR25-131 | 7th September 2025
Anand Kumar Narayanan

Hyperdeterminants are hard in four dimensions

Hyperdeterminants are high dimensional analogues of determinants, associated with tensors of formats generalizing square matrices. First conceived for $2\times 2\times 2$ tensors by Cayley, they were developed in generality by Gelfand, Kapranov and Zelevinsky. Yet, hyperdeterminants in three or more dimensions are long conjectured to be VNP-Hard to compute, akin ... more >>>


TR24-122 | 28th June 2024
Antoine Joux, Anand Kumar Narayanan

A high dimensional Cramer's rule connecting homogeneous multilinear equations to hyperdeterminants

Revisions: 1

We present a new algorithm for solving homogeneous multilinear equations, which are high dimensional generalisations of solving homogeneous linear equations. First, we present a linear time reduction from solving generic homogeneous multilinear equations to computing hyperdeterminants, via a high dimensional Cramer's rule. Hyperdeterminants are generalisations of determinants, associated with tensors ... more >>>




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