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commuting matrices (Definition)




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"commuting matrices" is owned by Algeboy. [ full author list (4) ]
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See Also: simultaneous triangularisation of commuting matrices over any field, common eigenvector of a diagonal element cross-section

Keywords:  diagonalizable, triangularizable
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Cross-references: addition, abelian, nilpotent group, even, generalized eigenspaces, identity matrix, sum, diagonalize, maps, induction, scalar, diagonal matrix, diagonal, diagonalizable, finite dimensional, transformations, finite set, preserve, eigenvalue, eigenspace, invariant, subspace, implication, eigenvalues, field, extension, simultaneous triangularisation of commuting matrices over any field, equivalent, matrices, represent, basis, fix, dimension, finite, vector space, linear transformations, properties
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This is version 17 of commuting matrices, born on 2006-05-07, modified 2007-08-05.
Object id is 7906, canonical name is CommutingMatrices.
Accessed 9001 times total.

Classification:
AMS MSC15A04 (Linear and multilinear algebra; matrix theory :: Linear transformations, semilinear transformations)

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induction proof by scineram on 2009-03-19 11:15:52
One step in the proof I fail to understand. When the operators are restricted to an eigenspace of one of them why are they still diagonalizable?
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