Titlebook: Mathematical Bridges; Titu Andreescu,Cristinel Mortici,Marian Tetiva Textbook 2017 Springer Science+Business Media LLC 2017 Real Analysis.

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Some Applications of the Hamilton-Cayley Theorem,n. The purpose of this chapter is to present a powerful theorem due to Hamilton and Cayley that gives an even stronger relation between a matrix and its characteristic polynomial: in a certain sense, the matrix is a “root” of its characteristic polynomial. After presenting a proof of this theorem, we investigate some interesting applications.

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Jacket

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Equivalence Relations on Groups and Factor Groups,Let . be a group with identity denoted by . and let ∅ ≠ . ⊆ . satisfy the implications:a) ., . ∈ . ⇒ . ∈ .;b) . ∈ . ⇒ .. ∈ ..

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Density,We say that a set . is . . if any open interval of real numbers contains elements from .. One of the practicalities of dense sets follows from the fact that two continuous functions from . to . are equal if they are equal on a dense subset of ..

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Uniform Continuity,We say that a function .: . ⊆ . → . is . if for all . > 0, there exists .(.) > 0 such that: