Rank of Jordan canonical form

Hi sir, I was practicing on the 2006 paper and I was wondering what the “rank” meant for Jordan canonical forms. I’d appreciate your help.



Rank is a notion that we use for any linear map, and is defined as the dimension of its image. If the map is given by a matrix, it is also the dimension of the column space. If two matrices represent the same linear map, that is, are similar, then they have the same rank. In particular, the rank of the Jordan canonical form is the same as the rank of the original matrix. One important fact to review is the formula relating the rank and nullity of a linear map.



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: