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- W1497193031 abstract "We show that Csanky's fast parallel algorithm for computing the characteristic polynomial of a matrix can be formalized in the logical theory LAP, and can be proved correct in LAP from the principle of linear independence. LAP is a natural theory for reasoning about linear algebra introduced in [8]. Further, we show that several principles of matrix algebra, such as linear independence or the Cayley-Hamilton Theorem, can be shown equivalent in the logical theory QLA. Applying the separation between complexity classes $textbf{AC}^0[2]subsetneqtextbf{DET}(text{GF}(2))$, we show that these principles are in fact not provable in QLA. In a nutshell, we show that linear independence is “all there is” to elementary linear algebra (from a proof complexity point of view), and furthermore, linear independence cannot be proved trivially (again, from a proof complexity point of view)." @default.
- W1497193031 created "2016-06-24" @default.
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- W1497193031 date "2005-01-01" @default.
- W1497193031 modified "2023-10-16" @default.
- W1497193031 title "Feasible Proofs of Matrix Properties with Csanky’s Algorithm" @default.
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- W1497193031 doi "https://doi.org/10.1007/11538363_34" @default.
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