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2. ♯P-completeness of 01-permanent - Wikipedia

   en.wikipedia.org/wiki/%E2%99%AFP-completeness_of...

   The #P-completeness of 01-permanent, sometimes known as Valiant's theorem, [1] is a mathematical proof about the permanent of matrices, considered a seminal result in computational complexity theory. [2] [3] In a 1979 scholarly paper, Leslie Valiant proved that the computational problem of computing the permanent of a matrix is #P-hard, even if ...

3. Permanent (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Permanent_(mathematics)

   Permanent (mathematics) In linear algebra, the permanent of a square matrix is a function of the matrix similar to the determinant. The permanent, as well as the determinant, is a polynomial in the entries of the matrix. [1] Both are special cases of a more general function of a matrix called the immanant.

4. Computing the permanent - Wikipedia

   en.wikipedia.org/wiki/Computing_the_permanent

   Computing the permanent. In linear algebra, the computation of the permanent of a matrix is a problem that is thought 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 ...

5. Hafnian - Wikipedia

   en.wikipedia.org/wiki/Hafnian

   The hafnian of an adjacency matrix of a graph is the number of perfect matchings (also known as 1-factors) in the graph. This is because a partition of into subsets of size 2 can also be thought of as a perfect matching in the complete graph . The hafnian can also be thought of as a generalization of the permanent, since the permanent can be ...

6. Symmetric successive over-relaxation - Wikipedia

   en.wikipedia.org/wiki/Symmetric_successive_over...

   Symmetric successive over-relaxation. In applied mathematics, symmetric successive over-relaxation (SSOR), [1] is a preconditioner. If the original matrix can be split into diagonal, lower and upper triangular as then the SSOR preconditioner matrix is defined as. It can also be parametrised by as follows.

7. Rotation matrix - Wikipedia

   en.wikipedia.org/wiki/Rotation_matrix

   Noting that any identity matrix is a rotation matrix, and that matrix multiplication is associative, we may summarize all these properties by saying that the n × n rotation matrices form a group, which for n > 2 is non-abelian, called a special orthogonal group, and denoted by SO(n), SO(n,R), SO n, or SO n (R), the group of n × n rotation ...