A canonical basis for the matrix transformation X → AXB

Trampus, A.

doi:10.1016/0022-247x(66)90068-0

Cited by 15 publications

(2 citation statements)

References 2 publications

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“…In the case of finite dimensions, the Jordan decomposition of M = A ⊗ I + I ⊗ B has been completely described [17,18,26]. It is proved that if A and B are both Jordan blocks, then M is not a single Jordan block unless H or K is of dimension one.…”

Section: Introductionmentioning

confidence: 98%

Reducing subspaces of tensor products of weighted shifts

Guo

Wang

2015

Sci. China Math.

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A unilateral weighted shift A is said to be simple if its weight sequence {αn} satisfies ∇ 3 (α 2 n ) = 0 for all n 2. We prove that if A and B are two simple unilateral weighted shifts, then A ⊗ I + I ⊗ B is reducible if and only if A and B are unitarily equivalent. We also study the reducing subspaces of A k ⊗ I + I ⊗ B l and give some examples. As an application, we study the reducing subspaces of multiplication operators M z k +αw l on function spaces.

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Section: Introductionmentioning

confidence: 98%

Reducing subspaces of tensor products of weighted shifts

Guo

Wang

2015

Sci. China Math.

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“…Also j(m, n) = j(n, m), and ~( m , n) = n(n, m). When x(F) = 0 a Jordan basis for S of the type (10) was specified by Trampus [ l l ] (see Theorem 3); in this case I, = m + n + 1 -2r (1 I r I r,) and so ~( m , n) is the identity permutation r(ro) of { 1,2,. . .…”

Section: Introductionmentioning

confidence: 99%

On the jordan form of the tensor product over fields of prime characteristic

Norman¹

1995

Linear and Multilinear Algebra

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L-et 4. B denote the companion matrice\ of the polynomials rm. u" ovcr a field r ofprime order r, and let i. p be 11011-~efo elements oidn extension field K of F. The Jordan torm of the tensor product ( I ! t A ) @ (pi t B) of in\ertibleJordan matrices ovcr K is determmed vla an equivalent study oithe niipotent transformation 5 of rn x n matricer X over F, where (X)S = A T X I-XB. Ubing mod~de-theoretic concepts a Jordan bas18 for S 18 spccificd recursively ~n terms of the representations of m and n in the scale of p, znd rednction formulae for the ?!em-ntnrv divisor? of S 2 r e estah!ished.

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Kronecker bases for linear matrix equations, with application to two-parameter eigenvalue problems

Košir

1996

Linear Algebra and its Applications

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A canonical basis for the matrix transformation X → AXB

Cited by 15 publications

References 2 publications

Reducing subspaces of tensor products of weighted shifts

Reducing subspaces of tensor products of weighted shifts

On the jordan form of the tensor product over fields of prime characteristic

Kronecker bases for linear matrix equations, with application to two-parameter eigenvalue problems

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