text: charactristic equation in linear algebra? if i have the matrix         a=    2   -1   -1  -1    2   -1 -1   -1    2  then how can i found the charactristic equation of a, becouse each time i found diffrenet answer depending on the book you use, the characteristic equation of a matrix a is the determinenat of a-xi or of xi-a. sometimes the greek letter lambda is used in place of x, but i won't do that here. in your case, you are looking for the determinant of 2-x -1 -1 -1 2-x -1 -1 -1 2-x  if you expand by the first row, you get (2-x)[(2-x)^2 -1] -(-1)[(-1)(2-x) -1] +(-1)[1-(-1)(2-x)]  which is  (2-x)^3-(2-x) -3+x -3+x =8-12x+6x^2-x^3 -2+x-6+2x =-9x+6x^2-x^3  now, to find the eigenvalues, you set the characteristic equation to 0 to get 0=-x(9-6x+x^2) =-x(x-3)^2,  so x=0,3 are eigenvalues with 3 repeated.  i hope this helps!