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

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

    Any square matrix = can be viewed as the adjacency matrix of a directed graph, with representing the weight of the edge from vertex to vertex .Then, the permanent of is equal to the sum of the weights of all cycle-covers of the graph; this is a graph-theoretic interpretation of the permanent.

  3. Computing the permanent - Wikipedia

    en.wikipedia.org/wiki/Computing_the_permanent

    While the compression operator maps the class of 1-semi-unitary matrices to itself and the classes of unitary and 2-semi-unitary ones, the compression-closure of the 1-semi-unitary class (as well as the class of matrices received from unitary ones through replacing one row by an arbitrary row vector — the permanent of such a matrix is, via ...

  4. Hafnian - Wikipedia

    en.wikipedia.org/wiki/Hafnian

    The hafnian of a symmetric matrix is defined as ⁡ = {,},, where is the set of all partitions of the set {,, …,} into subsets of size . [2] [3]This definition is similar to that of the Pfaffian, but differs in that the signatures of the permutations are not taken into account.

  5. Matrix (composite) - Wikipedia

    en.wikipedia.org/wiki/Matrix_(composite)

    Asphalt concrete, which is often used in the construction of roads, has a matrix called bitumen. Mud (wattle and daub) has observed considerable use. [6] Epoxy is utilized as a structural glue or structural matrix material in the aerospace industry. Epoxy resin is, when cured, nearly transparent.

  6. Hadamard's maximal determinant problem - Wikipedia

    en.wikipedia.org/wiki/Hadamard's_maximal...

    Hadamard's maximal determinant problem, named after Jacques Hadamard, asks for the largest determinant of a matrix with elements equal to 1 or −1. The analogous question for matrices with elements equal to 0 or 1 is equivalent since, as will be shown below, the maximal determinant of a {1,−1} matrix of size n is 2 n−1 times the maximal determinant of a {0,1} matrix of size n−1.

  7. Definite matrix - Wikipedia

    en.wikipedia.org/wiki/Definite_matrix

    In mathematics, a symmetric matrix with real entries is positive-definite if the real number is positive for every nonzero real column vector , where is the row vector transpose of . [1] More generally, a Hermitian matrix (that is, a complex matrix equal to its conjugate transpose) is positive-definite if the real number is positive for every nonzero complex column vector , where denotes the ...

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