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Some basic algebraic relations in the order‐reduction of large‐scale systems by aggregation
Author(s) -
YingPing Zheng
Publication year - 1981
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660020107
Subject(s) - generalization , rank (graph theory) , matrix similarity , reduction (mathematics) , mathematics , transformation (genetics) , algebraic number , matrix (chemical analysis) , similarity (geometry) , order (exchange) , algebra over a field , scale (ratio) , pure mathematics , discrete mathematics , combinatorics , computer science , mathematical analysis , artificial intelligence , biochemistry , chemistry , materials science , geometry , image (mathematics) , finance , partial differential equation , economics , composite material , gene , physics , quantum mechanics
In this paper, we prove conditions for the existence of a full‐rank matrix K which satisfies the aggregation relations (4)–(6). These conditions are convenient for checking and offer some rules for selecting K. Theorem 3 shows the properties of the matrix F in the aggregated model. It is actually a generalization of the important algebraic theorem on the similarity transformation of matrices.