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...

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

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

^{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...

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

matrix A ∈ Z m × n {\displaystyle A\in \mathbb {Z} ^{m\times n}} has a (row) Hermite normal form H {\displaystyle H} if there is a square unimodular matrix...

of the Gram matrix, a matrix with entries (ai, aj), where the elements ai form a basis for the lattice. An integral lattice is unimodular if its determinant...

matrices, although this use is discouraged. GCD matrix Unimodular matrix Wilson matrix Integer Matrix at MathWorld Hanson, Robert (1982). "Integer Matrices...

Ray transfer matrix analysis (also known as ABCD matrix analysis) is a mathematical form for performing ray tracing calculations in sufficiently simple...

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...

isomorphic. A polynomial matrix over a field with determinant equal to a non-zero element of that field is called unimodular, and has an inverse that...

{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...

vector length on a given vector machine. The unimodular transformation approach uses a single unimodular matrix to describe the combined result of a sequence...

to extend to the general case the notion of a unimodular matrix by calling unimodular a square matrix whose determinant is a unit. This means that the...

a unimodular form is one for which the determinant of the associate matrix is a unit (for example 1), hence the term; note that a form whose matrix determinant...

entries), an invertible matrix is a matrix that has an inverse that is also an integer matrix. Such a matrix is called a unimodular matrix for distinguishing...

the matrix. For this reason, regular matroids are sometimes also called unimodular matroids. The equivalence of regular matroids and unimodular matrices...

Jerusalem (the Knights Hospitaller) The human stomach or abdomen Totally Unimodular Matrix, in mathematics Tumbuka language (ISO 639-2 and 639-3 language code...

not true, except for some special cases (e.g. problems with totally unimodular matrix specifications.) In all cases, though, the solution quality of the...

matrix similarity. The row echelon form is a canonical form, when one considers as equivalent a matrix and its left product by an invertible matrix....

the n-dimensional torus and the automorphism T is represented by a unimodular matrix A then T is ergodic if and only if no eigenvalue of A is a root of...

following list of properties: It is unimodular; i.e., it can be generated by the columns of a certain 24×24 matrix with determinant 1. It is even; i.e...

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...

automorphism, which is an automorphism of a torus given by a square unimodular matrix having no eigenvalues of absolute value 1. The set of the points with...

matroid is regular if and only if it can be represented by a totally unimodular matrix. Rota's conjecture states that, for every finite field F, the F-linear...

to prove that an integer programming problem whose constraint matrix is totally unimodular and whose right-hand side is integer, has integer basic solutions...

elements are integers. It is unimodular, meaning that it is integral, and can be generated by the columns of an 8×8 matrix with determinant ±1 (i.e. the...

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...

balanced matrix is balanced. Moreover, any 0-1 matrix that is totally unimodular is also balanced. The following matrix is a balanced matrix as it does...