Title :
The proof complexity of linear algebra
Author :
Soltys, Michael ; Cook, Stephen
Author_Institution :
Dept. of Comput. & Software, McMaster Univ., Hamilton, Ont., Canada
Abstract :
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.
Keywords :
computational complexity; linear algebra; Cayley-Hamilton theorem; linear algebra; matrix identities; propositional proof complexity; Computer science; Educational institutions; Galois fields; Lagrangian functions; Linear algebra; Logic; Matrices; Parallel algorithms; Polynomials;
Conference_Titel :
Logic in Computer Science, 2002. Proceedings. 17th Annual IEEE Symposium on
Print_ISBN :
0-7695-1483-9
DOI :
10.1109/LICS.2002.1029841
