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A Formula for the Determinant  Nicholas Pippenger
;  Date: 
1 Jun 2022  Abstract:  We give a formula for the determinant of an $n imes n$ matrix with entries
from a commutative ring with unit. The formula can be evaluated by a
"straightline program" performing only additions, subtractions and
multiplications of ring elements; in particular it requires no divisions or
conditional branching (as are required, for example, by Gaussian elimination).
The number of operations performed is bounded by a fixed power of $n$,
specifically $O(n^4log n)$. Furthermore, the operations can be partitioned
into "stages" in such a way that the operands of the operations in a given
stage are either matrix entries or the results of operations in earlier stages,
and the number of stages is bounded by a fixed power of the logarithm of $n$,
specifically $Oig((log n)^2ig)$.  Source:  arXiv, 2206.00134  Services:  Forum  Review  PDF  Favorites 


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