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In this paper, we decompose (under unitary similarity) the Kronecker sum $A\boxplus A$ ($=A\otimes I+I\otimes A$) into a direct sum of irreducible matrices, when $A$ is a $3\times3$ matrix. As a consequence we identify $\mathcal{K}(A\boxplus A)$ as the direct sum of several full matrix algebras as predicted by Artin--Wedderburn theorem, where $\mathcal{K}(T)$ is the unital algebra generated by $T$ and $T^{*}$.
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참고문헌 (33)
참고문헌 신청
William B. Arveson / 1970 / Unitary invariants for compact operators / Bulletin of the American Mathematical Society 76(1):88~91
R. Bellman / 1970 / Introduction to Matrix Analysis / McGraw-Hill Book Co
J. Brewer / 1978 / Kronecker products and matrix calculus in system theory / IEEE Transactions on Circuits and Systems 25(9):772~781
Richard A. Brualdi / 1985 / Combinatorial verification of the elementary divisors of tensor products / Linear Algebra and its Applications 71:31~47
J.A. Dias da Silva / 1990 / A note on the minimal polynomial of the Kronecker sum of two linear operators / Linear Algebra and its Applications 141:283~287
R. Bellman / 1970 / Introduction to Matrix Analysis / McGraw-Hill Book Co
J. Brewer / 1978 / Kronecker products and matrix calculus in system theory / IEEE Transactions on Circuits and Systems 25(9):772~781
Richard A. Brualdi / 1985 / Combinatorial verification of the elementary divisors of tensor products / Linear Algebra and its Applications 71:31~47
J.A. Dias da Silva / 1990 / A note on the minimal polynomial of the Kronecker sum of two linear operators / Linear Algebra and its Applications 141:283~287
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