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The Cayley–Hamilton and Frobenius theorems via the Laplace transform

✍ Scribed by William A. Adkins; Mark G. Davidson

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
88 KB
Volume
371
Category
Article
ISSN
0024-3795

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✦ Synopsis

The Cayley-Hamilton theorem on the characteristic polynomial of a matrix A and Frobenius' theorem on minimal polynomial of A are deduced from the familiar Laplace transform formula L(e At ) = (sI -A) -1 . This formula is extended to a formal power series ring over an algebraically closed field of characteristic 0, so that the argument applies in the more general setting of matrices over a field of characteristic 0.

📜 SIMILAR VOLUMES

The initial- and final-value theorems in
The initial- and final-value theorems in Laplace transform theory
✍ Bernard Rasof 📂 Article 📅 1962 🏛 Elsevier Science 🌐 English ⚖ 549 KB

The initial-and final-value theorems, generally neglected in Laplace transform theory, for some purposes are among the most powerful results in that subject. Here are advanced some useful applications of these theorems: ~,,e show how they may be employed as necefsar~ checks on the accuracy of respon