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Prove. For two vectors X and Y


                ole.gif   



Proof. Let



                             ole1.gif   



and



                             ole2.gif   



and let a be any real number. We first derive the identity


                         ole3.gif


as follows:


             ole4.gif

                         ole5.gif

                         ole6.gif

                         ole7.gif

                         ole8.gif

                         ole9.gif


Now a quadratic polynomial in a is greater than or equal to zero for all real values of a if and only if its discriminant is less than or equal to zero. Thus


             ole10.gif


or


             ole11.gif


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