Theorems on Inner Product Space: Part-1 #
Theorems-1 #
Let be inner product space over a field and be a orthogonal subset of non null vectors of . If and then
(a) is orthogonal to each
(b) where , .
Proof: Given that be a orthogonal subset of non null vectors of the inner product space over the field .
Let and
where
To prove
To prove
First we prove that
Let
Lastly we prove that
Let
Hence