July 22, 2002 to July 25, 2002
Michael Soltys , McMaster University
Stephen Cook , University of Toronto
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.
Michael Soltys, Stephen Cook, "The Proof Complexity of Linear Algebra", LICS, 2002, Proceedings 17th Annual IEEE Symposium on Logic in Computer Science, Proceedings 17th Annual IEEE Symposium on Logic in Computer Science 2002, pp. 335, doi:10.1109/LICS.2002.1029841