Compute the Jordan canonical form of a given matrix

Compute the Jordan Canonical Forms of the matrices A = \begin{bmatrix} 5 & 4 & 1 \\ -1 & 0 & 0 \\ -3 & -4 & 1 \end{bmatrix} and B = \begin{bmatrix} 3 & 4 & 2 \\ -2 & -3 & -1 \\ -4 & -4 & -3 \end{bmatrix}.


Let P = \dfrac{1}{2} \begin{bmatrix} 0 & 0 & 1 \\ -3 & -4 & -1 \\ -2 & 0 & -2 \end{bmatrix} and Q = \dfrac{1}{2} \begin{bmatrix} 1 & 2 & 0 \\ 1 & 0 & 0 \\ 4 & 4 & 2 \end{bmatrix}. Evidently then P^{-1}AP = \begin{bmatrix} 2 & 1 & 0 \\ 0 & 2 & 1 \\ 0 & 0 & 2 \end{bmatrix} and Q^{-1}BQ = \begin{bmatrix} -1 & 0 & 0 \\ 0 & -1 & 1 \\ 0 & 0 & -1 \end{bmatrix} are in Jordan canonical form. (We used WolframAlpha for the computations; see here and here.)

Post a comment or leave a trackback: Trackback URL.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: