Low-Rank Equations

Definition ∞ Low-Rank Equations are mathematical expressions that involve matrices where the number of linearly independent rows or columns, known as the rank, is considerably smaller than the matrix’s overall dimensions. These equations are utilized in various fields to simplify complex systems by identifying and leveraging underlying structural properties. In computational mathematics, solving or manipulating low-rank equations can lead to significant efficiency gains compared to general matrix operations. They represent a compressed form of information.
Context ∞ In advanced cryptography, particularly within zero-knowledge proof systems like SNARKs and STARKs, low-rank equations are instrumental for achieving computational efficiency. They allow for the compression of large computations into smaller, verifiable proofs. Researchers frequently explore methods to transform complex problems into low-rank representations to optimize proof generation and verification times. News in this domain often highlights new techniques that improve the practical applicability of these cryptographic primitives.