Linear… algebra?

Let A\in M_n(k) be an n\times n matrix with coefficients in k a field of characteristic 0. Then \mathrm{tr}(A)=0 if and only if there exist matrices X,Y\in M_n(k) such that A = [X,Y]=XY-YX.

Advertisements
Linear… algebra?

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