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M-dimensional Cayley-Hamilton theorem

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1 Author(s)
Theodorou, N.J. ; Dept. of Electr. Eng., Nat. Tech. Univ. of Athens

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

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Automatic Control, IEEE Transactions on  (Volume:34 ,  Issue: 5 )