Unimodular polynomial matrix information

unimodular polynomial matrix is a square polynomial matrix whose inverse exists and is itself a polynomial matrix. Equivalently, a polynomial matrix A...

mathematics, unimodular may refer to any of the following: Unimodular lattice Unimodular matrix Unimodular polynomial matrix Unimodular form Unimodular group...

polynomial matrix or matrix of polynomials is a matrix whose elements are univariate or multivariate polynomials. Equivalently, a polynomial matrix is...

matrices are sometimes called integral matrices, although this use is discouraged. GCD matrix Unimodular matrix Wilson matrix Integer Matrix at MathWorld...

{Z} } , this means that the determinant is +1 or −1. Such a matrix is called unimodular. The determinant being multiplicative, it defines a group homomorphism...

efficiently solvable, most notably problems where the constraint matrix is totally unimodular and the right-hand sides of the constraints are integers or –...

univariate polynomials over a field. In this case, the extended Euclidean algorithm may be used for computing the above unimodular matrix; see Polynomial greatest...

solution is integral.}}\end{aligned}}} Thus, if the matrix A {\displaystyle A} of an ILP is totally unimodular, rather than use an ILP algorithm, the simplex...

triangular matrix is simply the product of its diagonal elements, which are all 1 for both Ln and Un. In other words, matrices Sn, Ln, and Un are unimodular, with...

transposition. An m by n matrix A with integer entries has a (row) Hermite normal form H if there is a square unimodular matrix U where H=UA and H has the...

matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries...

A.M.H. (1989). "A short proof of Tutte's characterization of totally unimodular matrices". Linear Algebra and Its Applications. 114–115: 207–212. doi:10...

although the two forms define the same polynomial. By contrast, the existence of Jordan canonical form for a matrix is a deep theorem. According to OED and...

In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, for which only...

the (lm + ln + mn) × (lmn) defining matrix of this system. Note that this matrix is generally not totally unimodular. Nonetheless, it was shown in that...

functions of even unimodular lattices An even unimodular lattice L in Rn is a lattice generated by n vectors forming the columns of a matrix of determinant...

and simpler proof of the characterization of unimodular matrices by forbidden minors. There is a polynomial time algorithm for testing whether a matroid...

take integer values. This is because the constraint matrix of the fractional LP is totally unimodular – it satisfies the four conditions of Hoffman and...

Equivalently a matroid is regular if it can be represented by a totally unimodular matrix (a matrix whose square submatrices all have determinants equal to 0, 1...

by a unimodular matrix. The Smith normal form of M is a matrix S = U M V , {\displaystyle S=UMV,} where U and V are unimodular, and S is a matrix such...

Jacobian matrix is a matrix whose entries are the partial derivatives of some polynomials. 2.  The Jacobian ideal of a quotient of a polynomial ring by...

exponent, up to a factor of −1/2, involves the simplest (unimodular, symmetric) symplectic matrix in Sp(2,R). That is, ( x , y ) M ( x y )   ,   {\displaystyle...

^{n}-(-\varphi )^{-n}}{\sqrt {5}}}.} The matrix A has a determinant of −1, and thus it is a 2 × 2 unimodular matrix. This property can be understood in terms...

two bases for lattice L {\displaystyle {\mathfrak {L}}} , there exist unimodular matrices U 1 {\displaystyle U_{1}} such that B 1 = B 2 U 1 − 1 , B 2 =...

polygons or two-dimensional polytopes are normal. If A is a totally unimodular matrix, then the convex hull of the column vectors in A is a normal polytope...

quippian rational integral function A polynomial. reciprocal The reciprocal of a matrix is the adjugate matrix. reciprocant 1.  A contravariant of a ternary...