I think it could be easier getting first the image.
I need to do a matrix and without the image (really complex) I think it's near impossible.
The Pauli group is a mathematical concept that was first introduced and defined through matrix calculations, rather than through drawings or diagrams. The concept of the Pauli group is based on a set of 2x2 matrices, known as the Pauli matrices, which were first introduced by physicist Wolfgang Pauli in the 1920s to describe the behavior of elementary particles.
The Pauli matrices are defined as follows:
σ_x = [ 0 1 ]
[ 1 0 ]
σ_y = [ 0 -i ]
[ i 0 ]
σ_z = [ 1 0 ]
[ 0 -1 ]
These matrices have several important properties, including that they are Hermitian (equal to their own conjugate transpose) and unitary (their inverse is equal to their conjugate transpose). These properties make them useful for describing quantum states and operations.
The Pauli group is a group of operations that can be performed on a quantum system using the Pauli matrices. It is generated by the tensor product of the Pauli matrices with themselves, and it has several important applications in quantum information processing and quantum computing.
While diagrams and drawings are sometimes used to visualize the operations of the Pauli matrices and the Pauli group, the concept itself was first defined and developed through matrix calculations and algebraic operations.
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