help me find basis and dimension

I don't know!!

help me !

use matlab :

find basis and dimension intersection  and sum of two subspace F and G!

Thanks a lot!

[Walter Roberson]

How would you do this in linear algebra ?

Answer 1

[Roger Stafford]

Assume that a subspace is represented as being the subspace spanned by a set of columns vectors.

To find a basis of the "sum" of F and G (presumably you mean the subspace spanned by their union) just combine the sets of column vectors and then use 'orth'. The number of columns of the result would be your dimension.

To find a basis for their intersection use 'null' on each, find the basis of the union of these as above, then do 'null' on the result of that.

Warning: The 'orth' and 'null' functions are numerical and round-off errors may cause some of the above results to be inaccurate.