the degree of characteristic polynomial [closed]

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!

-
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
show 1 more comment

closed as too localized by Deane Yang, George Lowther, Gerry Myerson, Captain Oates, Anton GeraschenkoMar 18 '11 at 2:00

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.