THE DIMENSION OF MATRICES (MATRIX PENCILS) WITH GIVEN JORDAN (KRONECKER) CANONICAL-FORMS

被引：52

作者：

DEMMEL, JW

EDELMAN, A

机构：

[1] UNIV CALIF BERKELEY,DEPT MATH,BERKELEY,CA 94720

[2] MIT,DEPT MATH,CAMBRIDGE,MA 02139

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 1995年 / 230卷

基金：

美国国家科学基金会;

关键词：

D O I：

10.1016/0024-3795(93)00362-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The set of n by n matrices with a given Jordan canonical form defines a subset of matrices in complex n(2) dimensional space. We analyze one classical approach and one new approach to count the dimension of this set. The new approach is based upon and meant to give insight into the staircase algorithm for the computation of the Jordan canonical form as well as the occasional failures of this algorithm. We extend both techniques to count the dimension of the more complicated set defined by the Kronecker canonical form of an arbitrary rectangular matrix pencil A - lambda B.

引用

页码：61 / 87

页数：27

共 19 条

[1]

Arnold V.I., 1971, RUSS MATH SURV+, V26, P29

[2] THE JORDAN CANONICAL FORM - AN OLD PROOF [J].

BRUALDI, RA .

AMERICAN MATHEMATICAL MONTHLY, 1987, 94 (03) :257-267

[3] ACCURATE SOLUTIONS OF ILL-POSED PROBLEMS IN CONTROL-THEORY [J].

DEMMEL, J ;

KAGSTROM, B .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1988, 9 (01) :126-145

[4]

FAIRGRIEVE T, 1986, THESIS U TORONTO CAN

[5]

Gantmacher F., 1959, THEORY MATRICES, VI

[6]

Golub G.H., 1996, MATH GAZ, VThird

[7] AN ALGORITHM FOR NUMERICAL COMPUTATION OF THE JORDAN NORMAL-FORM OF A COMPLEX MATRIX [J].

KAGSTROM, B ;

RUHE, A .

ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 1980, 6 (03) :398-419

[8] RGSVD - AN ALGORITHM FOR COMPUTING THE KRONECKER STRUCTURE AND REDUCING SUBSPACES OF SINGULAR A-LAMBDA-B PENCILS [J].

KAGSTROM, B .

SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1986, 7 (01) :185-211

[9]

KAGSTROM B, 1985, BIT, V24, P568

[10]

Kublanovskaya Vera, 1966, USSR COMP MATH MATH, V6, p[611, 1]

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