In linear algebra , the computation of the permanent of a matrix is a problem that is known to be more difficult than the computation of the determinant of a matrix despite the apparent similarity of the definitions.

The permanent is defined similarly to the determinant, as a sum of products of sets of matrix entries that lie in distinct rows and columns. However, where the determinant weights each of these products with a ±1 sign based on the parity of the set , the permanent weights them all with a +1 sign.

While the determinant can be computed in polynomial time by Gaussian elimination , the permanent cannot. In computational complexity theory , a theorem of Valiant states that computing permanents is #P-hard , and even #P-complete for matrices in which all entries are 0 or 1. Valiant (1979) This puts the computation of the permanent in a class of problems believed to be even more difficult to compute than NP . It is known that computing the permanent is impossible for logspace-uniform ACC 0 circuits.( Allender & Gore 1994 )

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In linear algebra, the computation of the permanent of a matrix is a problem that is known to be more difficult than the computation of the determinant of a matrix ...

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In linear algebra , the computation of the permanent of a matrix is a problem that is known to be more difficult than the computation of the determinant of a matrix despite the apparent similarity of the definitions.

The permanent is defined similarly to the determinant, as a sum of products of sets of matrix entries that lie in distinct rows and columns. However, where the determinant weights each of these products with a ±1 sign based on the parity of the set , the permanent weights them all with a +1 sign.

While the determinant can be computed in polynomial time by Gaussian elimination , the permanent cannot. In computational complexity theory , a theorem of Valiant states that computing permanents is #P-hard , and even #P-complete for matrices in which all entries are 0 or 1. Valiant (1979) This puts the computation of the permanent in a class of problems believed to be even more difficult to compute than NP . It is known that computing the permanent is impossible for logspace-uniform ACC 0 circuits.( Allender & Gore 1994 )

When I set out to research the out-of-control harassment problem in gamer culture, I never dreamed my mother would be caught up in the middle of it all.

We humans are far more complex than the news headlines and clickbait would have you believe. Let the Narratively newsletter be your guide.

A whistleblower puts his life on the line to defy Soviet aggression. Sixty years later, this forgotten story of subterfuge, smears and suspicious death has never felt more timely.

In linear algebra , the computation of the permanent of a matrix is a problem that is known to be more difficult than the computation of the determinant of a matrix despite the apparent similarity of the definitions.

The permanent is defined similarly to the determinant, as a sum of products of sets of matrix entries that lie in distinct rows and columns. However, where the determinant weights each of these products with a ±1 sign based on the parity of the set , the permanent weights them all with a +1 sign.

While the determinant can be computed in polynomial time by Gaussian elimination , the permanent cannot. In computational complexity theory , a theorem of Valiant states that computing permanents is #P-hard , and even #P-complete for matrices in which all entries are 0 or 1. Valiant (1979) This puts the computation of the permanent in a class of problems believed to be even more difficult to compute than NP . It is known that computing the permanent is impossible for logspace-uniform ACC 0 circuits.( Allender & Gore 1994 )

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