Assume a positive definite scalar product. let v1, ... vn be non zero elements which are mutually perpendicular, i.e. <vi, vj> = 0 if i not equal to j. show that they are linearly independent.
Assume a positive definite scalar product. let v1, ... vn be non zero elements which are mutually perpendicular, i.e. <vi, vj> = 0 if i not equal to j. show that they are linearly independent.
Hint
Let a1v1+.....+anvn = 0
So, <a1v1+.....+anvn,v1>=0