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: