Question

In Lecture 11, Prof. Strang rejects the union of U and S and suggests using the "sum". What is the sum of the two vector spaces? Sum isn't an operation that makes sense for two sets of vectors. He does say that its combinations of S and U, but I'm still bothered by his use of "sum" and a "+" sign for the two sets of vectors. Maybe if he had said that it was the "span" of vectors in either S or U, it would be clearer. Am I being unreasonable about this? I was hoping to find some kind of mention in the text that would allow interpreting a "+" in the manner suggested for vector spaces.

Answer 1

\[S \cup U\] is the union of elements in S and U , whereas S+U is all linear combinations of elements in S and U

Answer 2

Thats why in that lecture you get dimension of 9 for S+U . was this helpful ?

Answer 3

I found WikiBooks: Linear Algebra/Combining Subspaces ( http://en.wikibooks.org/wiki/Linear_Algebra/Combining_Subspaces ) where this is treated and they actually state "The notation, writing the " + " between sets in addition to using it between vectors, fits with the practice of using this symbol for any natural accumulation operation". They also make a formal definition of "sum" as "the span of the union of the subspaces". This was the only place I've seen this custom mentioned.

Answer 4

ya thats what i also told , "sum" as "the span of the union of the subspaces"

Answer 5

friend was it helpful ??