How to find the normalized form of an eigenvector if that eigenvector has a complex element ,forexample find the normalized form of [1/√2;i/√2;1/√2]?

1 Answer
May 24, 2018

See below

Explanation:

Typically a vector is normalised as:

  • #(bb v )/(abs bb v)#

And the dot product is used:

  • #|bb v|^2 = bb v * bb v = sum_i v_1*v_1 + v_2 * v_2 + ...#

For vectors with complex entries the dot product is re-defined. In this particular case it is:

  • # bb v * bb v = sum_i v_1* bar v_1 + v_2 * bar v_2 + ...#

More generally:

#bb A * bb B = sum_i A_i*bar B_i #