Gram-Schmidt Process: Solve for V & x

[Tonyt88]

Homework Statement

V = span(S) where S = {(1, i, 0), ((1-i), 2, 4i)}, and x = ((3+i), 4i, -4)

Obtain the orthogonal basis, then normalize for the orthonormal basis, and then compute the Fourier coefficients.

Homework Equations

v2 = w2 - (<w2,v1>)(v1)/(||v1||²)

The Attempt at a Solution

So using this above equation, I get ||v1||² to equal zero because 1 + i² = 1 - 1 = 0, thus I'm dividing by zero, so where do I go from here, or am I miscalculating somewhere?

 

[robphy]

How do you compute the square-norm of a complex number?

 

[astrosona]

Ok this is what you did wrong:

||v1||² = v1* . v1 = (1, i, 0)*. (1, i, 0) = 1+(-i)(i)=1+1=2