Find basis for R3 relative to which the matrix for T is diagonal:

T[x1, x 2, x3] = [-2x1 + x2 - x3, x1 - 2x2 - x3, -x1 - x2 - 2x3]

Printable View

- Jun 23rd 2008, 10:33 AMchadlyterFinding a basis
Find basis for R3 relative to which the matrix for T is diagonal:

T[x1, x 2, x3] = [-2x1 + x2 - x3, x1 - 2x2 - x3, -x1 - x2 - 2x3] - Jun 23rd 2008, 10:41 AMMoo
Hello :p

Find the matrix T of the transformation.

$\displaystyle T=\begin{pmatrix} -2&1&-1 \\ 1&-2&-1 \\ -1&-1&-2 \end{pmatrix}$

Step 1 :

find the eigenvalues

Step 2 :

find the eigenvectors associated to each eigenvalue

Step 3 :

it's done :P

---------------------------

How to find eigenvalues :

Find the characteristic polynomial, defined as :

$\displaystyle \chi_T(\lambda)=det(T-\lambda I_3)$

The eigenvalues will be the__roots__of the characteristic polynomial.

----------------------------

Comment :

Hmmm I have to check it out :(