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Hi, there!

Let $A$ be an $n \times n$ sparse matrix with an average of $d$ nonzero entries in each row, and let $poly(A)$ be the characteristic polynomial of the matrix $A$, I was just wondering there is any relations between the degree of $poly(A)$ and $d$. Thanks!

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Either you and I have a different definition of characteristic polynomial, or I do not understand the question at all. –  quid Mar 18 '11 at 1:10
Umm, poly(A)=det(A-xI) is a degree $n$ polynomial. –  David Hill Mar 18 '11 at 1:11
What about the number of nonzero coefficients of $poly(A)$? –  Vít Tuček Mar 18 '11 at 1:12
my definition of characteristic polynomial is as follows : en.wikipedia.org/wiki/Characteristic_polynomial –  jane Mar 18 '11 at 1:13
@Jane, according to that definition, the degree is $n$, independently of the matrix coefficients. –  Mariano Suárez-Alvarez Mar 18 '11 at 1:17
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closed as too localized by Deane Yang, George Lowther, Gerry Myerson, Yemon Choi, Anton Geraschenko Mar 18 '11 at 2:00

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