Definition ∞ Arbitrary Matrices are mathematical constructs consisting of numerical elements arranged in rows and columns, without specific structural constraints such as symmetry or diagonality. These matrices serve as fundamental tools in linear algebra and various computational applications. Their general form allows for broad applicability in representing data transformations and system states. They are often utilized in complex calculations where no predefined structural properties are assumed.
Context ∞ In advanced cryptographic research, particularly concerning zero-knowledge proofs and secure multi-party computation, arbitrary matrices find application as components within more elaborate mathematical frameworks. They can represent the underlying algebraic structures of computations that need to be verified or kept private. The efficiency of cryptographic protocols can depend on how these matrices are manipulated and compressed, which is a key area of ongoing theoretical and practical investigation.
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