Rectangular and polar representations of a complex matrix

Leang S. Shieh, Jason S.H. Tsai, Norman P. Coleman

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


This paper presents some new definitions of the real and imaginary parts and the associated amplitude and phase of a real or complex matrix. Computational methods, which utilize the properties of the matrix sign function and the principal nth root of a complex matrix, are given for finding these quantities. A geometric series method is newly developed for finding the approximant of the matrix-valued function of tan −1(X), which is the principal branch of the arc tangent of the matrix X. Several illustrative examples are presented.

Original languageEnglish
Pages (from-to)1825-1838
Number of pages14
JournalInternational Journal of Systems Science
Issue number10
Publication statusPublished - 1987

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Theoretical Computer Science
  • Computer Science Applications


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