Properties of Eigens Let Ai,(i=1,2,...,n)be the eigenvalues of A and zi0 be the corresponding eigenvectors,then, ●∑21Xi=1ai where is the trace of A,denoted by tr(A); ·I1λi=|A where|A is determinant of A. ·A-a≤∑=1aal e.g. 01 1/20-1 Copyright©2011，NA⊙Yin Last Modification:Oct.2011 6Properties of Eigens Let λi ,(i = 1, 2, . . . , n) be the eigenvalues of A and xi 6= 0 be the corresponding eigenvectors, then, • Pn i=1 λi = Pn i=1 aii where Pn i=1 aii is the trace of A, denoted by tr(A); • Qn i=1 λi = |A| where |A| is determinant of A. • |λ − aii| ≤ Pn j=1,j6=i |aij|. e.g. A =   1 0 −1 1 3 0 1/2 0 −1   Copyright c 2011, NAYin Last Modification: Oct. 2011 6