Let U=(13i3−i). What is U†?
Explicitly indicate multiplication with a * symbol. For instance, you should write 3*i+2 instead of 3i+2.
To find the conjugate transpose (†), we need to find the complex conjugate of each element of the matrix and then transpose the matrix.
Given U = (13i3 - i)
First, let's find the complex conjugate of each element by changing the sign of the imaginary part:
Complex conjugate of 13i3 = 13i*-3 = -39i
Complex conjugate of -i = i (no change because the imaginary part is already negative)
So the complex conjugate of U = (-39i -i)
Next, we need to transpose the matrix. Since U is a 1x2 matrix, its transpose will be a 2x1 matrix.
Transposing the complex conjugate of U:
( -39i )
( -i )
Therefore, U† = ( -39i )
( -i )