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Examples ofinvariant theory
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The study of branching rules is important in classicalinvarianttheoryand its modern counterpart, algebraic combinatorics.
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This example is from Wikipedia and may be reused under a CC BY-SA license.To remedy this, classicalinvarianttheoryalso considered "relative invariants", which were forms invariant up to a scale factor.
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This example is from Wikipedia and may be reused under a CC BY-SA license.For geometric terms used ininvarianttheorysee the glossary of classical algebraic geometry.
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This example is from Wikipedia and may be reused under a CC BY-SA license.He was known as the king ofinvarianttheory.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Butinvarianttheoryworks in this context only over an algebraically closed field.
From theCambridge English Corpus
His main research interest is theinvarianttheoryof finite groups.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Although the technique is deceptively simple, it has applications in many areas of abstract mathematics: in particular to algebraic geometry,invarianttheory, and representation theory.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Invarianttheoryof infinite groups is inextricably linked with the development of linear algebra, especially, the theories of quadratic forms and determinants.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Another way, connected withinvarianttheoryis via the polarization identity for a symmetric tensor.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Ininvarianttheory, the symmetric group acts on the variables of a multi-variate function, and the functions left invariant are the so-called symmetric functions.
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This example is from Wikipedia and may be reused under a CC BY-SA license.He made fundamental contributions to matrix theory,invarianttheory, number theory, partition theory and combinatorics.
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This example is from Wikipedia and may be reused under a CC BY-SA license.A time-reversalinvarianttheoryis more logical and elegant.
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This example is from Wikipedia and may be reused under a CC BY-SA license.In other words, a scaleinvarianttheoryis one without any fixed length scale (or equivalently, mass scale) in the theory.
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This example is from Wikipedia and may be reused under a CC BY-SA license.One of the main goals ofinvarianttheorywas to solve the finite basis problem.
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This example is from Wikipedia and may be reused under a CC BY-SA license.He also worked oninvarianttheoryand projective differential geometry.
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This example is from Wikipedia and may be reused under a CC BY-SA license.In a separate development the symbolic method ofinvarianttheory, an apparently heuristic combinatorial notation, has been rehabilitated.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Modern research ininvarianttheoryof finite groups emphasizes effective results, such as explicit bounds on the degrees of the generators.
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This example is from Wikipedia and may be reused under a CC BY-SA license.This fact is one of the foundations ofinvarianttheory.
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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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