Answer to Question #272586 in Functional Analysis for Prathibha Rose

Question #272586

Let x1 x2 … . . xn, be an orthonormal set in X and π‘˜1 ,π‘˜2,. … … … 

π‘˜nbe scalars

having absolute value 1. Then π‘˜1x1 + π‘˜ 2x 2+ β‹― … π‘˜ nxn= x1 + β‹― +Β 

xn



1
Expert's answer
2021-12-06T07:46:47-0500

a set of vectors is orthogonal if every pair of vectors is orthogonal

A set of vectors is orthonormal ifΒ it is an orthogonal set having the property that every vector is a unit vectorΒ 


since "k_n=1" then:

"\ud835\udc58 _nx_n=x_n"

so, statement "\ud835\udc58_1x_1 + \ud835\udc58 _2x_ 2+ \u22ef \u2026 \ud835\udc58_ nx_n= x_1 + \u22ef + x_n" is true



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