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单位模; 单位模的

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  • Unimodular matrix - Wikipedia
    In mathematics, a unimodular matrix M is a square integer matrix having determinant +1 or −1 Equivalently, it is an integer matrix that is invertible over the integers: there is an integer matrix N that is its inverse (these are equivalent under Cramer's rule)
  • Unimodular Matrix - from Wolfram MathWorld
    More generally, a matrix A with elements in the polynomial domain F [x] of a field F is called unimodular if it has an inverse whose elements are also in F [x]
  • 1 Totally Unimodular Matrices - Stanford University
    De nition 1 (Totally Unimodular Matrix) A matrix A is totally unimodular if every square submatrix has determinant 0, +1, or 1 In particular, this implies that all entries are 0 or 1
  • Unimodular lattice - Wikipedia
    In geometry and mathematical group theory, a unimodular lattice is an integral lattice of determinant 1 or −1 For a lattice in n -dimensional Euclidean space, this is equivalent to requiring that the volume of any fundamental domain for the lattice be 1
  • Lecture 10: Totally Unimodular Matrices
    A matrix A is totally unimodular (TU) if every square submatrix of A has determi-nant 0, 1, or −1 Note All entries of a TU matrix should be in {0, ±1} The next proposition is a simple, yet powerful property of totally unimodular matrices Recall that a square matrix is nonsingular if its determinant is non-zero (i e , it is full-ranked)
  • Small Matrices with Small Inverses: Unimodular Zerofree Cases
    Abstract We consider unimodular matrices M such that neither M nor M 1 contain zero entries Matrices typically exhibit a trade-off: small M imply large M 1 We investigate rare cases where both remain small, classify these matrices up to symmetry, and discuss aspects of this balanced setting
  • Unimodular Matrices - Andrea Minini
    Unimodular Matrices A square matrix M of order m is called unimodular if all its entries are integers and its determinant is either +1 or -1: $$ \det (M) = \pm 1 $$
  • linear algebra - How to construct unimodular matrices? - Mathematics . . .
    Definition: An $n \times n$ matrix $A$ with integer entries is called unimodular if $\det A = \pm 1$ For $n=2$, if $a, b$ are coprime integers, by Euclid's algorithm, there exist $x, y$ such that $ax-by=1$
  • Lecture 6: Totally Unimodular Matrices
    Unimodular Matrix A unimodular matrix M is a square integer matrix with determinant +1 or −1 Equivalently, it is an integer matrix that is invertible over the integers, i e , there is an integer matrix M’ which is its inverse (these are equivalent under Cramer's rule)
  • Lecture 10: Totally Unimodular Matrices and Applications
    De nition 1 A matrix A is totally unimodular (TU) if every square submatrix of A has determi-nant 0; 1; or 1 Note All entries of a TU matrix should be in f0; 1g The next proposition is a simple, yet powerful property of totally unimodular matrices Recall that a square matrix is nonsingular if its determinant is non-zero (i e , it is full





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