EXPANSION PROBLEMS FOR HERMITION MATRICES WHILE MAINTAINING THE EIGENVALUES
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For given Hermition matrix A, in this paper, we will study the existence of an expansion Hermition matrix A of A while maintaining the eigenvalues of A. For any proper subset ｛λj1, λj2, … , λjk｝of the spectrum σ(A) = (λ1, λ2, …, λn) of A, we explicitly show the existence of an expansion A^ of A whose spectrum contains all λj1, λj2, … , λjk· Moreover, we show that there exists a 2-step expansion A of A whose spectrum contains all eigenvalues of A, that is, σ(A) ⊂ σ(A).
Abstract
For given Hermition matrix A, in this paper, we will study the existence of an expansion Hermition matrix A of A while maintaining the eigenvalues of A. For any proper subset ｛λj1, λj2, … , λjk｝of the spectrum σ(A) = (λ1, λ2, …, λn) of A, we explicitly show the existence of an expansion A^ of A whose spectrum contains all λj1, λj2, … , λjk· Moreover, we show that there exists a 2-step expansion A of A whose spectrum contains all eigenvalues of A, that is, σ(A) ⊂ σ(A).
참고문헌 (7)
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