Question

Linear Algebra: Can someone please explain the direct sum of subspaces? I'm having trouble understanding it.

Answer 1

what exactly?

Answer 2

http://solitaryroad.com/c222.html
It is hard to explain, and the website does a better job than me.

Answer 3

The symbol is written as a + with a circle around it. It is called the direct sum. My textbook doesn't explain it well.

Answer 4

if you have two disjoint subspaces U, V then you can form the direct sum which is all vectors of the form u + v with u in U and V in V

Answer 5

i mean you can always form a sum of vectors of subspaces but if the subspaces are disjoint, that is their only element in common is the zero vector, then the "direct sum" is the span of U and V and any element in the direct sum can be written UNIQUELY as u + v with u in U and v in V

Answer 6

pk51 has a better answer

Answer 7

Okay, I think I'm getting a better grasp on it. Thanks for the help and resource!