On the interlacing property for singular values and eigenvalues
نویسندگان
چکیده
منابع مشابه
On computing accurate singular values and eigenvalues . . .
[15] D. O'Leary and G. W. Stewart. Computing the eigenvalues and eigenvectors of symmetric arrowhead matrices. [17] A. Sameh and D. Kuck. A parallel QR algorithm for symmetric tridiagonal matrices. [21] Zhonggang Zeng. The acyclic eigenproblem can be reduced to the arrowhead one. [22] Hongyuan Zha. A two-way chasing scheme for reducing a symmetric arrowhead matrix to tridiagonal form. Scientic ...
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for some nonzero vector x called an eigenvector. This is equivalent to writing (λI − A)x = 0 so, since x 6= 0, A− λI must be singular, and hence det(λI − A) = 0. From the (complicated!) definition of determinant, it follows that det(λI−A) is a polynomial in the variable λ with degree n, and this is called the characteristic polynomial. By the fundamental theorem of algebra (a nontrivial result)...
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We prove results concerning the interlacing of eigenvalues of principal submatrices of strictly totally positive (STP) matrices.
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We prove results concerning the interlacing of eigenvalues of principal submatrices of strictly totally positive matrices. §
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Chi-Kwong Li Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187-8795, USA E-mail: [email protected] We briefly describe some recent results on inequalities relating the eigenvalues of the sum of Hermitian or real matrices, and how to use these them inequalities relating the eigenvalues and singular values of a matrix and its submatrices. These results are joint ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1987
ISSN: 0024-3795
DOI: 10.1016/0024-3795(87)90136-4