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unipotent element
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In mathematics, a unipotent element r of a ring R is one such that r − 1 is a nilpotent element; in other words, (r − 1)n is zero for some n.
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Article
17 sectionsContents
- Definition
- Definition with matrices
- Definition with ring theory
- Definition with representation theory
- Examples
- U<sub>''n''</sub>
- G<sub>a</sub><sup>''n''</sup>
- Kernel of the Frobenius
- Classification of unipotent groups over characteristic 0
- Remarks
- Unipotent radical
- Decomposition of algebraic groups
- Characteristic 0
- Characteristic ''p''
- Jordan decomposition
- See also
- References
In mathematics, a unipotent element r of a ring R is one such that r − 1 is a nilpotent element; in other words, (r − 1)n is zero for some n.
In particular, a square matrix M is a unipotent matrix if and only if its characteristic polynomial P(t) is a power of t − 1. Thus all the eigenvalues of a unipotent matrix are 1.
Connections
block matrix
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isomorphism
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eigenvectors and eigenvalues
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diagonal matrix
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triangular matrix
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invertible matrix
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adjacency matrix
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algebraic group
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abelian variety
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unimodular matrix
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band matrix
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definite matrix
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affine variety
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mathematics
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statistics
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International Standard Book Number
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complex number
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digital object identifier
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matrix
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group
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