The Lorentz group and the Kronecker product of matrices

The group $SL(2,\mathbb{C})$ of all complex $2\times 2$ matrices with determinant one is closely related to the $\boldsymbol{\mathcal{L}}_{+}^\uparrow$ real $4\times 4$ representing restricted Lorentz transformations. This relation, sometimes called spinor map, fundamental importance in relativistic quantum mechanics and has applications also general relativity. In this paper we show how map may be expressed terms pure matrix algebra by including Kronecker product between formalism. so-obtained formula for manipulated used study