Let be subspaces of where is a vector space with inner product and show that
No idea how to show this!
Hi-Outlines of the proof.
1.
This is easy to show.
2. So if we show that dimension of LHS = dimension of RHS we are done
3.
This can again be shown easily
4. dim( ) + dim( ) = dim( ) =
We will use this result directly. This is applicable for any sub-space W in V.
5. dim( ) = dim( ) + dim( ) - dim( )
We will use this result directly. This is applicable for any sub-paces S,W in V.
Let dim( ) = s, dim( )=w, dim( ) = i, dim( ) = u
so,
dim( ) = dim( )+dim( ) - dim( )
=
=
= dim( )
Hence we are done.