Folks,(adsbygoogle = window.adsbygoogle || []).push({});

I am looking at my notes. Wondering where the highlighted comes from.

Prove that a finite orthogonal set is lineaarly independent

let u=(x_1,x_2,x_n) bee an orthogonal set set of vectors in an ips.

To show u is linearly independent suppose

Ʃ ##\alpha_i x_i=0## for i=1 to n

Fix any j=1 and consider <Ʃ##\alpha_i x_i, x_j##> i=1 to n

then

0=<Ʃ##\alpha_i x_i, x_j##> i=1 to n

=Ʃ<##\alpha_i x_i, x_j##> i=1 to n

=Ʃ##\alpha_i <x_i, x_j>## i=1 to n

=##\alpha_j <x_j, x_j>## since u is an orthonormal set

Where does this line come from? Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Orthogonal Sets

**Physics Forums | Science Articles, Homework Help, Discussion**