Thread: matrices

how come no invertible 3x3 matrix E for which E^-1AE is diagonal??? thanks!!!!!!!!!!!!

Originally Posted by eleahy

how come no invertible 3x3 matrix E for which E^-1AE is diagonal??? thanks!!!!!!!!!!!!

Your question is meaningless if you don't redact it in a clear way and if you don't tell us what is A

Tonio

sorry didnt think that had anything to do with the last question my bad!!!
let A=the 3x3 matrix (3 4 -1
-1 -2 1
3 9 0)

eigenvalues ar 2 and -3

Originally Posted by eleahy

sorry didnt think that had anything to do with the last question my bad!!!
let A=the 3x3 matrix (3 4 -1
-1 -2 1
3 9 0)

eigenvalues ar 2 and -3

So it seems to be that you have to prove that the matrix A is not diagonalizable...well, you know that a matrix is diagonalizable iff there's a basis (of the vector space on which it acts) formed by eigenvectors of the matrix: have you already evaluated all the eigenvectors of the matrix corresponding to its eigenvalues?

Tonio

i think so i got -4x+5y=0 as one and 4x-5y=0 as the other usinng the eigenvalue 7 which i think means itany non zero vector in which 4x=5y is an eigenvecotr
the second one corresponding to the eigenvalue 2 is 5x+5y=0 andn 4x+4y=0 therefroe any non zero vector in which 4x=5y is an eigenvecotr corresponding to the eigenvalue -2

i think that is right but i thought for example -4x+5y=0 and 4x-5y=0 should be the same ???