The Cayley-Hamilton and Frobenius theorems via the Laplace transform (Q1406289)
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scientific article; zbMATH DE number 1978111
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Cayley-Hamilton and Frobenius theorems via the Laplace transform |
scientific article; zbMATH DE number 1978111 |
Statements
The Cayley-Hamilton and Frobenius theorems via the Laplace transform (English)
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9 September 2003
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It is shown that the Cayley-Hamilton theorem on the characteristic polynomial of a matrix \(A\) and the Frobenius theorem on the minimal polynomial of \(A\) are a consequence of the Laplace transform formula \({\mathcal L}(e^{AT})= (SI- A)^{-1}\). This formula is extended to a power series ring over an algebraically closed field of characteristic \(0\).
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Cayley-Hamilton theorem
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Frobenius theorem
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Laplace transform
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matrix exponential
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characteristic polynomial
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minimal polynomial
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formal power series
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