Jump to content

Span

hkus10
in Homework Help

Featured Replies

Let T be the set of all matrics of the form AB - BA, where A and B are nxn matrics. Show that span T is not Mnn.

 

1) does "span T is not Mnn" mean that Mnn does not span T?

 

Thanks

Let T be the set of all matrics of the form AB - BA, where A and B are nxn matrics. Show that span T is not Mnn.

 

1) does "span T is not Mnn" mean that Mnn does not span T?

 

Thanks

 

No it means that the set of all linear combinations of elements of T does not include all of Mnn.

 

One presumes that by Mnn you mean all nxn matrices, so the problem is to show that the space spanned by commutators is not all linear operators on n-space.

 

To do that you might want to look for an invariant shared by commutators that is not a property of all operators.

Archived

This topic is now archived and is closed to further replies.

Go to topic listing

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.

Configure browser push notifications
Chrome (Android)
  1. Tap the lock icon next to the address bar.
  2. Tap Permissions → Notifications.
  3. Adjust your preference.
Chrome (Desktop)
  1. Click the padlock icon in the address bar.
  2. Select Site settings.
  3. Find Notifications and adjust your preference.