“Cayley-Hamilton Theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Cayley-Hamilton Theorem

释义

Cayley-Hamilton Theorem

Given

(1)

then

(2)

where I is the Cayley

verified this identity for

and 3 and postulated that it wastrue for all

. For

, direct verification gives


			(3)

(8)

The Cayley-Hamilton theorem states that a

Matrix A is annihilated by its CharacteristicPolynomial

, which is monic of degree

.
References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, p. 1117, 1979.

Segercrantz, J. ``Improving the Cayley-Hamilton Equation for Low-Rank Transformations.'' Amer. Math. Monthly 99, 42-44, 1992.

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