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...
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mathematics, unimodular may refer to any of the following: Unimodular lattice Unimodular matrix Unimodular polynomial matrix Unimodular form Unimodular group...
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unimodular polynomial matrix is a square polynomial matrix whose inverse exists and is itself a polynomial matrix. Equivalently, a polynomial matrix A...
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Hermite normal form (category Matrix normal forms)
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...
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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...
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vector length on a given vector machine. The unimodular transformation approach uses a single unimodular matrix to describe the combined result of a sequence...
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List of named matrices (redirect from List of matrix)
matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries...
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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...
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Fibonacci sequence (section Matrix form)
^{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...
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Bilinear form (redirect from Unimodular form)
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...
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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...
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Jerusalem (the Knights Hospitaller) The human stomach or abdomen Totally Unimodular Matrix, in mathematics Tumbuka language (ISO 639-2 and 639-3 language code...
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matrices are sometimes called integral matrices, although this use is discouraged. GCD matrix Unimodular matrix Wilson matrix Integer Matrix at MathWorld...
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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...
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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....
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not true, except for some special cases (e.g. problems with totally unimodular matrix specifications.) In all cases, though, the solution quality of the...
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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...
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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...
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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...
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the matrix. For this reason, regular matroids are sometimes also called unimodular matroids. The equivalence of regular matroids and unimodular matrices...
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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...
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with good properties (such as short nearly orthogonal vectors) and a unimodular matrix U {\displaystyle U} . The public key is another basis of the lattice...
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Ray transfer matrix analysis (also known as ABCD matrix analysis) is a mathematical form for performing ray tracing calculations in sufficiently simple...
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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...
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Leech lattice (section Using a Paley matrix)
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...
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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...
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Haar measure (redirect from Unimodular group)
} . The left and right Haar measures are the same only for so-called unimodular groups (see below). It is quite simple, though, to find a relationship...
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Cramer's rule (section Finding inverse matrix)
to prove that an integer programming problem whose constraint matrix is totally unimodular and whose right-hand side is integer, has integer basic solutions...
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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...
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using computer algebra systems. Her constructions include extremal even unimodular lattices in 48, 56, and 72 dimensions and an extremal 3-modular lattice...
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