Error in Vector Multiplication of Complex Numbers

Hello,

I am running into a strange error in vector multiplication. Let's say I have the two variables, a = 2i and b = 1. It is clear that a^2+b^2 = -4+1 = -3.

However, when I write them in vector form, [a,b]*[a,b]', Matlab gives me an wrong answer, that is, [a,b]*[a,b]' = 5.

Does anyone know what's happening here, or do I miss some logics behind?

Thank you!

[Stephen23]

"Does anyone know what's happening here, or do I miss some logics behind?"

You are using conjugate tranpose, but you should use element-wise transpose:

>> a = 2i;
>> b = 1;
>> [a,b]' % conjugate transpose (what you are doing)
ans =
   0 - 2i
   1 - 0i
>> [a,b].' % transpose (what you should be doing)
ans =
   0 + 2i
   1 + 0i

Note you can trivially avoid the transpose anyway, by defining the vector as a column:

>> [a;b]
ans =
   0 + 2i
   1 + 0i

[Yuling Shen]

Hi Stephen,

Thanks very much for the explanation! This helps a lot!

Answer 1

[Andrei Bobrov]

>> [a,b]*[a;b]
ans =
    -3
>> [a,b]*[a,b].'
ans =
    -3
>> [a,b]*transpose([a,b])
ans =
    -3
>> [a,b].'
ans =
            0 +          2i
            1 +          0i
>> [a,b]'
ans =
            0 -          2i
            1 +          0i
>> transpose([a,b])
ans =
            0 +          2i
            1 +          0i
>> ctranspose([a,b])
ans =
            0 -          2i
            1 +          0i
>> 

[Yuling Shen]

Many thanks for the answer!