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 Hermitian conjugate (also known as the adjoint) of a complex matrix or vector, we take the complex conjugate of each element and transpose the result. In this case, we have U=(13i3−i).
To find U†, let's break down the process step by step:
Step 1: Take the complex conjugate of each element in U.
- The complex conjugate of 13i is -13i.
- The complex conjugate of 3 is 3.
- The complex conjugate of -i is i.
So, the complex conjugate of U is (-13i 3 i).
Step 2: Transpose the complex conjugate of U.
- To transpose a matrix or vector, we simply switch its rows and columns.
Transposing (-13i 3 i) gives us the matrix:
(-13i)
(3)
(i)
Therefore, U† = (-13i 3 i).
Note: In the context of the original question, it is not necessary to indicate multiplication with a * symbol as used in algebraic expressions. The use of the * symbol is more relevant for expressions involving multiplication in programming or computer contexts.