On matrix equations X - A X F = C and X - A over(X, -) F = C

Ai Guo Wu; Hao Qian Wang; Guang Ren Duan

doi:10.1016/j.cam.2009.01.013

On matrix equations X - A X F = C and X - A over(X, -) F = C

Ai Guo Wu^*
, Hao Qian Wang
, Guang Ren Duan

^*Corresponding author for this work

Tsinghua University

Research output: Contribution to journal › Article › peer-review

39 Scopus citations

Abstract

With the help of the concept of Kronecker map, an explicit solution for the matrix equation X - A X F = C is established. This solution is neatly expressed by a symmetric operator matrix, a controllability matrix and an observability matrix. In addition, the matrix equation X - A over(X, -) F = C is also studied. An explicit solution for this matrix equation is also proposed by means of the real representation of a complex matrix. This solution is neatly expressed by a symmetric operator matrix, two controllability matrices and two observability matrices.

Original language	English
Pages (from-to)	690-698
Number of pages	9
Journal	Journal of Computational and Applied Mathematics
Volume	230
Issue number	2
DOIs	https://doi.org/10.1016/j.cam.2009.01.013
State	Published - 15 Aug 2009

Keywords

Controllability matrix
Kronecker map
Observability matrix
Real representation

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10.1016/j.cam.2009.01.013

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title = "On matrix equations X - A X F = C and X - A over(X, -) F = C",

abstract = "With the help of the concept of Kronecker map, an explicit solution for the matrix equation X - A X F = C is established. This solution is neatly expressed by a symmetric operator matrix, a controllability matrix and an observability matrix. In addition, the matrix equation X - A over(X, -) F = C is also studied. An explicit solution for this matrix equation is also proposed by means of the real representation of a complex matrix. This solution is neatly expressed by a symmetric operator matrix, two controllability matrices and two observability matrices.",

keywords = "Controllability matrix, Kronecker map, Observability matrix, Real representation",

author = "Wu, \{Ai Guo\} and Wang, \{Hao Qian\} and Duan, \{Guang Ren\}",

year = "2009",

month = aug,

day = "15",

doi = "10.1016/j.cam.2009.01.013",

language = "英语",

volume = "230",

pages = "690--698",

journal = "Journal of Computational and Applied Mathematics",

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T1 - On matrix equations X - A X F = C and X - A over(X, -) F = C

AU - Wu, Ai Guo

AU - Wang, Hao Qian

AU - Duan, Guang Ren

PY - 2009/8/15

Y1 - 2009/8/15

N2 - With the help of the concept of Kronecker map, an explicit solution for the matrix equation X - A X F = C is established. This solution is neatly expressed by a symmetric operator matrix, a controllability matrix and an observability matrix. In addition, the matrix equation X - A over(X, -) F = C is also studied. An explicit solution for this matrix equation is also proposed by means of the real representation of a complex matrix. This solution is neatly expressed by a symmetric operator matrix, two controllability matrices and two observability matrices.

AB - With the help of the concept of Kronecker map, an explicit solution for the matrix equation X - A X F = C is established. This solution is neatly expressed by a symmetric operator matrix, a controllability matrix and an observability matrix. In addition, the matrix equation X - A over(X, -) F = C is also studied. An explicit solution for this matrix equation is also proposed by means of the real representation of a complex matrix. This solution is neatly expressed by a symmetric operator matrix, two controllability matrices and two observability matrices.

KW - Controllability matrix

KW - Kronecker map

KW - Observability matrix

KW - Real representation

UR - https://www.scopus.com/pages/publications/67349254484

U2 - 10.1016/j.cam.2009.01.013

DO - 10.1016/j.cam.2009.01.013

M3 - 文章

AN - SCOPUS:67349254484

SN - 0377-0427

VL - 230

SP - 690

EP - 698

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

On matrix equations X - A X F = C and X - A over(X, -) F = C

Abstract

Keywords

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