On sharp frame diagonalization

https://doi.org/10.1016/j.laa.2012.09.030

Richards, Kendall C.

Denman, Richard T.

Futamura, Fumiko

2018-02-27

2018-02-27

2013

Denman, R. T., Futamura, F., & Richards, K. C. (March 01, 2013). On sharp frame diagonalization. Linear Algebra and Its Applications, 438, 5, 2210-2224.

https://collections.southwestern.edu/s/suscholar/item/239

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.

English

Linear Algebra and Its Applications

Frame

Diagonalization

Jordan canonical form

Article