Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0657.15008
Hong, YooPyo; Horn, Roger A.
A canonical form for matrices under consimilarity. (English)
[J] Linear Algebra Appl. 102, 143-168 (1988). ISSN 0024-3795

Complex $n\times n$ matrices A, B are said to be consimilar if $B=S\sp{- 1}A\bar S$ for some non-singular complex matrix S. This concept arises naturally from comparing the expressions for a semilinear transformation on an n-dimensional complex vector space in two different coordinate systems. The present paper gives a detailed survey, with an extensive bibliography, of the known results on consimilarity. A canonical form for A under consimilarity, closely related to the usual Jordan normal form for $A\bar A$, is described in section 3. Various applications are given in section 4. For example (Theorem 4.5), A and B are consimilar if, and only if, (a) $A\bar A$ and $B\bar B$ are similar and (b) $A,A\bar A,A\bar AA,...$ have the same respective ranks as $B,B\bar B,B\bar BB,...$. Again, it is noted that A is consimilar to $\bar A,$ $A\sp{\top}$ and $A\sp*$, and that every matrix is consimilar both to a real matrix and to a Hermitian matrix. Altogether, this is a useful and clearly written survey.
[G.E.Wall]

MSC 2000:: *15A21 Canonical forms, etc.
15A04 Linear transformations (linear algebra)

Keywords: semilinear transformation; consimilarity; canonical form; Jordan normal form

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]