Let V be a finite-dimensional inner product space with orthonormal basis {e.e.....en). (a) For any x...

 

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Let V be a finite-dimensional inner product space with orthonormal basis {e.e.....en). (a) For any x V show that x = (x,e) e + (x, e) e+ + (x.e) e. (b) For any x, y = V show that (x, y) = (x.es) (y,e) + (x.e) (yes) + + (x.en) (y.eu). (e) For any x V show that ||x2= |(x,e) + (x) ++1(x,c) = (x.e). What theorem from classical geometry does this generalize? Let V be a finite-dimensional inner product space with orthonormal basis {e.e.....en). (a) For any x V show that x = (x,e) e + (x, e) e+ + (x.e) e. (b) For any x, y = V show that (x, y) = (x.es) (y,e) + (x.e) (yes) + + (x.en) (y.eu). (e) For any x V show that ||x2= |(x,e) + (x) ++1(x,c) = (x.e). What theorem from classical geometry does this generalize?