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]

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- 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.

Step 1 :

find the eigenvalues

Step 2 :

find the eigenvectors associated to each eigenvalue

Step 3 :

it's done :P

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How to find eigenvalues :

Find the characteristic polynomial, defined as :

The eigenvalues will be the__roots__of the characteristic polynomial.

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Comment :

Hmmm I have to check it out :(