Sudoku, the Golden Ratio, Determinants, Eigenvectors and Matrices In $\mathbb Z$

The Sudoku game has gained much interest for a dozen years. It is now put in various magazines and mathematical research is more and more interested in it. This document aims at providing some newer information about the mathematical properties of the Sudoku, but not according to graphs' theory. We do not speak about the ``minimum number of clues,'' but about Sudokus' matrix interpretation: general properties of its determinant, in relation to eigenvalues; transpose; non-Hermitian character; neither symmetric nor antisymmetric character; non-normal character; non-orthogonal character when the matrix has a determinant of 0, conjecture when the determinant is not equal to 0; order; condition number.