Question

Prove: if u and v are vectors in an inner product space and c is a scalar, then =c

Answer 1

can't we just do it with algebra?\[<u\cdot cv>=<u_1,u_2,...,u_n>\cdot<cv_1,cv_2,...,cv_n>\]\[=cu_1v_1+cu_2v_2+\cdots+cu_nv_n=c(u_1v_1+u_2v_2+\cdots+u_nv_n)\]\[=c<u,v>\]I hope that is sufficient

Answer 2

that should be\[<u,cv>\]at the beginning, but you get the point...
off to class, later!

Answer 3

Thanks @TuringTest

Answer 4

K got it :D