I have the following vector z = ( x y ) . I also have...

Nelson Jennings

Nelson Jennings

Answered

2022-07-14

I have the following vector z = ( x y ) . I also have the function
f = ( 5 β x y 5 β x y )
I need to rewrite this such that x and y will be simply denoted as the vector z. The closest I am getting to is
f = 5 β ( 0 x y 0 ) z
I can't seem to rearrange this matrix however such that it can be written in terms of z.
I am starting to question whether what I am trying to do is even possible. Is it possible?

Answer & Explanation

Kitamiliseakekw

Kitamiliseakekw

Expert

2022-07-15Added 23 answers

There are many ways to write this. Here's one. For
z = [ x y ] ,
define
f ( z ) = ( z T σ x z ) [ 5 β / 2 5 β / 2 ] ,
where T denotes the transpose (so z T is a row vector), and σ x is a Pauli spin matrix, specifically
σ x = [ 0 1 1 0 ] .
Note that the quantity in parentheses is a number equal to xy.

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