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Title
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On sharp frame diagonalization
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Description
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https://doi.org/10.1016/j.laa.2012.09.030
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Creator
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Richards, Kendall C.
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Denman, Richard T.
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Futamura, Fumiko
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Date
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2018-02-27
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Date Available
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2018-02-27
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Date Issued
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2013
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Identifier
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Denman, R. T., Futamura, F., & Richards, K. C. (March 01, 2013). On sharp frame diagonalization. Linear Algebra and Its Applications, 438, 5, 2210-2224.
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uri
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https://collections.southwestern.edu/s/suscholar/item/239
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Abstract
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It was recently shown that if M = 1 ⊕ ··· ⊕ k ∈ Cn×n is a
Jordan matrix with k nontrivial Jordan blocks i, then M can be
frame diagonalized by embedding M into a diagonalizable matrix in
C(n+)×(n+) with = k. This naturally motivates a pursuit of the
best possible value of for which this is possible. Here, we use Lid-
skii’s Theorem on eigenvalue perturbations to construct diagonaliz-
ing frames for = k. := max{gmM(λ)|λ ∈ σ (M)}. Moreover, we verify that k. is sharp.
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Language
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English
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Publisher
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Linear Algebra and Its Applications
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Subject
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Frame
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Diagonalization
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Jordan canonical form
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Type
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Article
