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Examples ofunimodular
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Both groups consist ofunimodularmatrices which can be inverted by simple matrix multiplications requiring a very limited number of numerical operations.
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The coefficient matrix of the reduced system is not totallyunimodular.
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However, this is not possible in theunimodularcase of unweighted graphs.
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Appending such a row to a totallyunimodularmatrix preserves this property.
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Furthermore, the theta function of an evenunimodularlattice of rank "n" is actually a modular form of weight "n" /2.
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This example is from Wikipedia and may be reused under a CC BY-SA license.In order for the theory to work correctly, the 16 mismatched dimensions must be compactified on an even,unimodularlattice of rank 16.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Then (2) is the group ofunimodulartransformations which preserve the parity of each entry.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Given a finite-dimensional module over a commutative ring, the pairing may be injective (hence nondegenerate in the above sense) but notunimodular.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The matrix has a determinant of 1, and thus it is a 22unimodularmatrix.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Over a field, "unimodular" has the same meaning as "non-singular".
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This example is from Wikipedia and may be reused under a CC BY-SA license.Unimodularsimplicies are the smallest polytope in the world of normal polytopes.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Note that this matrix is generally "not" totallyunimodular.
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This example is from Wikipedia and may be reused under a CC BY-SA license.One common way of proving that a polyhedron is integral is to show that it is totallyunimodular.
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This example is from Wikipedia and may be reused under a CC BY-SA license.This is because the constraint matrix is totallyunimodular.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Another important application is in the theory of unitary representations ofunimodularlocally compact groups, where the theory has been applied to the regular representation and other closely related representations.
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This example is from Wikipedia and may be reused under a CC BY-SA license.This means that the determinant is invertible and implies thatunimodularmatrices are the invertible matrices such all entries of the inverse matrix belong to the domain.
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This example is from Wikipedia and may be reused under a CC BY-SA license.In other words these groups areunimodular.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Such a matrix is calledunimodular.
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This example is from Wikipedia and may be reused under a CC BY-SA license.These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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