The Proof Complexity of Linear Algebra

We introduce three formal theories of increasing strength for linear algebra in order to study the complexity of the concepts needed to prove the basic theorems of the subject. We give what is apparently the first feasible proofs of the Cayley-Hamilton theorem and other properties of the determinant, and study the propositional proof complexity of matrix identities.

• Type: Conference
• Year: 2002
• Where: LICS
• Authors: Michael Soltys, Stephen A. Cook
• Keywords: Automated Reasoning, Formal Theories, LICS 2002, Propositional Proof Complexity, first Feasible Proofs