Abstract
In this chapter we discuss the celebrated Cayley–Hamilton theorem, its reciprocal, as well as some of the most important applications of this theorem. We also give various formulae involving determinants and traces and we go over the Jordan canonical form theorem.
If \(A \in \mathcal{M}_{2}\left (\mathbb{C}\right )\) , then A 2 − Tr (A)A + (det A)I 2 = O 2 . Cayley–Hamilton
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Notes
- 1.
The problem states that any singular matrix is the limit of a sequence of nonsingular matrices.
References
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Pop, V., Furdui, O. (2017). The Cayley–Hamilton Theorem. In: Square Matrices of Order 2. Springer, Cham. https://doi.org/10.1007/978-3-319-54939-2_2
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DOI: https://doi.org/10.1007/978-3-319-54939-2_2
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