Theorem-1

Theorems on Inner Product Space: Part-1 Theorems-1  Let \(\pmb{ V}\) be inner product space over a field \(\pmb{ F}\) and \(\pmb{S=\{x_{1},x_{2},…,x_{k} \}}\) be a orthogonal subset of non null vectors of \(\pmb{ V}\). If \(\pmb{ x\in V-L(S)}\) and \(\pmb{y=x- \displaystyle\sum_{i=1}^{k} c_{i}x_{i}}\) then  (a)   \(\pmb{ x}\) is orthogonal to each \(\pmb{ x_{i}}\)  (b)   \(\pmb{...