A generalization of a class of test matrices

Author:

Herbold Robert J.

Abstract

We consider matrices of the following form: G n ( a 1 , a 2 , , a n 1 , b 1 , b 2 b n ) = {G_n}({a_1},{a_2}, \cdots ,{a_{n - 1}},{b_1},{b_2} \cdots {b_n}) = ( β i , j ) , 1 i ({\beta _{i,j}}),1 \leqq i , j n j \leqq n , where a 1 , , a n 1 , b 1 , , b n {a_1}, \cdots ,{a_{n - 1}},{b_1}, \cdots ,{b_n} are constants and \[ β i , j = b j ,   j i ;   β i j = a j ,   j > i . {\beta _i}_{,j} = {b_j},{\text { }}j \geqq i;{\text { }}{\beta _{ij}} = {a_j},{\text { }}j > i. \] We deduce in analytic form the determinant, inverse matrix, characteristic equation, and eigenvectors of G n {G_n} . Knowing these properties enables us to generate valuable test matrices by appropriately selecting the order and elements of G n {G_n} .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference1 articles.

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A Generalization of a Class of Matrices: Analytic Inverse and Determinant;Advances in Numerical Analysis;2011-12-01

2. On computer-algebra procedures that check for common eigenvectors or invariant subspaces;Computational Mathematics and Modeling;1998-10

3. Computational methods of linear algebra;Journal of Soviet Mathematics;1981

4. Testmatrizen mit maximaler Konditionszahl;Computing;1974-03

5. A collection of matrices for testing computational algorithms;USSR Computational Mathematics and Mathematical Physics;1971-01

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