0
$\begingroup$

I have this matrix $M$

$M = \begin{bmatrix} 1 & 1 & 1\\ 2 & 1 & -1\\ 0 & -1 & 1 \end{bmatrix}$

And I was asked to put it into Jordan Canonical Form.

I did this, and obtained

if $M$ = $SQS^{-1}$

Then $S = \begin{bmatrix} -3 & 0 & -1\\ 4 & -1 & -1\\ 2 & 1 & 0 \end{bmatrix}$

And $Q = \begin{bmatrix} -1 & 0 & 0\\ 0 & 2 & 1\\ 0 & 0 & 2 \end{bmatrix}$ is the matrix of jordan blocks

I am now asked to "find the appropriate transition matrix to the basis in which the the original matrix assumes its Jordan form." Needless to say I have no idea what it is asking and any clarification would be largely appreciated.

Gracias

$\endgroup$
0
$\begingroup$

You've already answered the question. $Q$ is the "Jordan canonical form", and $S^{-1}$ is "the appropriate transition matrix to the basis in which the original matrix assumes its normal form."

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.