Simple forms and invariant subspaces of H-expansive matrices

Fourie, Jan; Groenewald, G. J.; Rensburg, D.B. Janse van; Ran, André C. M.

doi:10.1016/j.laa.2014.11.022

Cited by 5 publications

(5 citation statements)

References 7 publications

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“…(so H ij = Hx j , x i ). Analogously to what has been done in [5] and [12], we already know the following:…”

Section: Proof We May Assume Based On Proposition 11 That In This Casementioning

confidence: 52%

“…for an invertible n × n matrix H (0) . By Section 2 in [5], (see also [12]), we have that H (0) i j = 0 for i + j ≤ n. Moreover, from A T HA = H we have that…”

Section: Proof We May Assume Based On Proposition 11 That In This Casementioning

confidence: 99%

“…We keep the convention that comma separated subindices indicate that we are working with 2 × 2 blocks. This convention was used by the authors in earlier papers [5,8,12] as well.…”

Section: Complex Unimodular Eigenvaluesmentioning

confidence: 99%

“…Our point of view is that we wish to bring the matrix A in (real) Jordan canonical form, and see what this implies for the matrix H representing the bilinear or sesquilinear form. The start of our considerations was the simple form for expansive matrices in an indefinite inner product, developed in [12] and [5].…”

Section: Introductionmentioning

confidence: 99%

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Canonical form for H-symplectic matrices

Groenewald

Rensburg

Ran

2018

Operator Theory, Analysis and the State Space Approach

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“…(so H ij = Hx j , x i ). Analogously to what has been done in [5] and [12], we already know the following:…”

Section: Proof We May Assume Based On Proposition 11 That In This Casementioning

confidence: 52%

“…for an invertible n × n matrix H (0) . By Section 2 in [5], (see also [12]), we have that H (0) i j = 0 for i + j ≤ n. Moreover, from A T HA = H we have that…”

Section: Proof We May Assume Based On Proposition 11 That In This Casementioning

confidence: 99%

“…We keep the convention that comma separated subindices indicate that we are working with 2 × 2 blocks. This convention was used by the authors in earlier papers [5,8,12] as well.…”

Section: Complex Unimodular Eigenvaluesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Canonical form for H-symplectic matrices

Groenewald

Rensburg

Ran

2018

Operator Theory, Analysis and the State Space Approach

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“…For some classes of matrices canonical forms do not exist, but simple forms can be deduced. This is the case for H-dissipative matrices, see [16], and for H-expansive matrices [4]. In several cases canonical forms or even simple forms are either very hard or impossible, see [13,15] for some results on H-hyponormal matrices.…”

Section: Introductionmentioning

confidence: 99%