scholarly journals A Hermitian canonical form for complex matrices under consimilarity

1990 ◽  
Vol 133 ◽  
pp. 1-19 ◽  
Author(s):  
Yoopyo Hong
1954 ◽  
Vol 6 ◽  
pp. 69-72 ◽  
Author(s):  
B. E. Mitchell

We consider the problem of finding a unique canonical form for complex matrices under unitary transformation, the analogue of the Jordan form (1, p. 305, §3), and of determining the transforming unitary matrix (1, p. 298, 1. 2). The term “canonical form” appears in the literature with different meanings. It might mean merely a general pattern as a triangular form (the Jacobi canonical form (8, p. 64)). Again it might mean a certain matrix which can be obtained from a given matrix only by following a specific set of instructions (1). More generally, and this is the sense in which we take it, it might mean a form that can actually be described, which is independent of the method used to obtain it, and with the property that any two matrices in this form which are unitarily equivalent are identical.


2014 ◽  
Vol 2 (1) ◽  
Author(s):  
Tatiana Klimchuk ◽  
Vladimir V. Sergeichuk

AbstractL. Huang [Consimilarity of quaternion matrices and complex matrices, Linear Algebra Appl. 331 (2001) 21–30] gave a canonical form of a quaternion matrix with respect to consimilarity transformations A ↦ ˜S


2017 ◽  
Vol 2 (1) ◽  
pp. 123-130 ◽  
Author(s):  
Tetiana Klymchuk

AbstractP. Van Dooren (1979) constructed an algorithm for computing all singular summands of Kronecker’s canonical form of a matrix pencil. His algorithm uses only unitary transformations, which improves its numerical stability. We extend Van Dooren’s algorithm to square complex matrices with respect to consimilarity transformations $\begin{array}{} \displaystyle A \mapsto SA{\bar S^{ - 1}} \end{array}$ and to pairs of m × n complex matrices with respect to transformations $\begin{array}{} \displaystyle (A,B) \mapsto (SAR,SB\bar R) \end{array}$, in which S and R are nonsingular matrices.


2018 ◽  
Vol 8 (3) ◽  
pp. 36-41
Author(s):  
Diep Do Thi Hong ◽  
Duong Le Phuoc ◽  
Hoai Nguyen Thi ◽  
Serra Pier Andrea ◽  
Rocchitta Gaia

Background: The first biosensor was constructed more than fifty years ago. It was composed of the biorecognition element and transducer. The first-generation enzyme biosensors play important role in monitoring neurotransmitter and determine small quantities of substances in complex matrices of the samples Glutamate is important biochemicals involved in energetic metabolism and neurotransmission. Therefore, biosensors requires the development a new approach exhibiting high sensibility, good reproducibility and longterm stability. The first-generation enzyme biosensors play important role in monitoring neurotransmitter and determine small quantities of substances in complex matrices of the samples. The aims of this work: To find out which concentration of polyethylenimine (PEI) exhibiting the most high sensibility, good reproducibility and long-term stability. Methods: We designed and developed glutamate biosensor using different concentration of PEI ranging from 0% to 5% at Day 1 and Day 8. Results: After Glutamate biosensors in-vitro characterization, several PEI concentrations, ranging from 0.5% to 1% seem to be the best in terms of VMAX, the KM; while PEI content ranging from 0.5% to 1% resulted stable, PEI 1% displayed an excellent stability. Conclusions: In the result, PEI 1% perfomed high sensibility, good stability and blocking interference. Furthermore, we expect to develop and characterize an implantable biosensor capable of detecting glutamate, glucose in vivo. Key words: Glutamate biosensors, PEi (Polyethylenimine) enhances glutamate oxidase, glutamate oxidase biosensors


Author(s):  
D. B. Hunter

1. Introduction. Let A[λ] be the irreducible invariant matrix of a general matrix of order n × n, corresponding to a partition (λ) = (λ1, λ2, …, λr) of some integer m. The problem to be discussed here is that of determining the canonical form of A[λ] when that of A is known.


2012 ◽  
Vol 437 (4) ◽  
pp. 1071-1088 ◽  
Author(s):  
Dimitrios Noutsos ◽  
Richard S. Varga
Keyword(s):  

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