For the Perron roots of square nonnegative matrices A, B, and A + D~BXD, where D is a diagonal matrix with positive diagonal entries, the inequality is proved under the assumption that A and B have a common unordered pair of nonorthogonal right and left Perron vectors. The case of equality is analy
Two inequalities for the Perron Root
โ Scribed by R.B. Bapat
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 352 KB
- Volume
- 85
- Category
- Article
- ISSN
- 0024-3795
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๐ SIMILAR VOLUMES
Let A โ R n,n and let ฮฑ and ฮฒ be nonempty complementary subsets of {1, . . . , n} of increasing integers. For ฮป > ฯ(A[ฮฒ]), we define the generalized Perron complement of A[ฮฒ] in A at ฮป as the matrix For the classes of the nonnegative matrices and of the positive semidefinite matrices, we study the
The eigenvalue problem for a symmetric persymmetric matrix can be reduced to two symmetric eigenvalue problems of lower order. In this paper, we find in which of these problems the Perron root of a nonnegative symmetric persymmetric matrix lies. This is applied to bound the Perron root of such class