- #1

- 2

- 0

Can anyone help guide me along in this proof?

- Thread starter zmdeez
- Start date

- #1

- 2

- 0

Can anyone help guide me along in this proof?

- #2

matt grime

Science Advisor

Homework Helper

- 9,395

- 3

- #3

- 2

- 0

- #4

matt grime

Science Advisor

Homework Helper

- 9,395

- 3

What is the span of a subset? iti s the set of all combinations

[tex]t_1x_1+\ldots t_nx_n[/tex]

for t_i in R (or the underlying field) and x_i in W

so W=span(W) means exactly that all finite combinations of elements of W are in W.

so we are trying to show that

W closed under combining (adding up) two elements of itself if and only if W is closed under combining a finite number of elements of itself.

Obvioulsy one way is simple: if i can add up any number of combinations of elements then i can in particular add up two of them. Conversely...?

- Last Post

- Replies
- 3

- Views
- 2K

- Last Post

- Replies
- 2

- Views
- 2K

- Last Post

- Replies
- 4

- Views
- 14K

- Last Post

- Replies
- 4

- Views
- 6K

- Replies
- 8

- Views
- 13K

- Replies
- 1

- Views
- 2K

- Last Post

- Replies
- 1

- Views
- 5K

- Replies
- 7

- Views
- 996

- Last Post

- Replies
- 2

- Views
- 3K

- Last Post

- Replies
- 8

- Views
- 15K