Minimal polynomial
The minimal polynomial of an n-by-n matrix A over a field F is the monic[?] polynomial p(x) over F such that p(A)=0.The following three statements are equivalent:
- λ∈F is a root of p(x),
- λ is a root of the characteristic polynomial of A,
- λ is an eigenvalue of A.
The multiplicity of a root λ of p(x) is the geometrical multiplicity of &lambda and is the size of the largest Jordan block[?] corresponding to &lambda.
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and manners. Hence, instead of longer applying to the empire the
Byzantine empire.
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their affairs into prominence, and we shall see a line of Latin princes
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CHAPTER XXXVI.
MOHAMMED AND THE SARACENS.
their surprising part in history, are, after the Hebrews, the most
deserts, the Arabs have never as a people bowed their necks to a foreign
subjugated by different races.
RELIGIOUS CONDITION OF ARABIA BEFORE MOHAMMED.--Before the reforms of
the ancient and most revered shrine of the Caaba, where was preserved a
were many followers of other faiths; for Arabia at this time was a land of
Jewish synagogue and the Christian church. The Jews especially were to be
the Roman persecutions. It was from the Jews and Christians, doubtless,
city of Mecca, about the year 570 of our era. He sprang from.
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