Title :
M-dimensional Cayley-Hamilton theorem
Author_Institution :
Dept. of Electr. Eng., Nat. Tech. Univ. of Athens
fDate :
5/1/1989 12:00:00 AM
Abstract :
The theorem states that every block square matrix satisfies its own m-D (m-dimensional, m⩾1) matrix characteristic polynomial. The exact statement and a simple proof of this theorem are given. The theorem refers to a matrix A subdivided into m blocks, and hence having dimension at least m. The conclusion is that every square matrix A with dimension M satisfies several m-D characteristic matrix polynomials with degrees N1 . . ., N m, such that N1+ . . . +Nm ⩽M
Keywords :
matrix algebra; multidimensional systems; polynomials; Cayley-Hamilton theorem; block square matrix; multidimensional systems; polynomial; Automatic control; Control systems; Extraterrestrial measurements; Frequency measurement; Limit-cycles; Polynomials; Regulators; Relays; Sampling methods; Tuning;
Journal_Title :
Automatic Control, IEEE Transactions on
