09-11U

The classification for the set of all Hadamard matrices with dimension 4x4 is performed on the basis of similarity. The properties of four Hadamard matrix types, namely, canonical, light, 50/50 and semicanonical ones are investigated. The necessary and sufficient condition for Hadamard matrices similarity according to the permutation matrixes is formulated. It is established the existence of 384 such matrixes belonging to 6 different classes. The every similar Hadamard matrices class is characterized by the eigenvalues spectrum. It is defined the three types of matrixes belonging to the every similarity class. Half-canonical Hadamard matrices the set of which as well consists of 384 basis matrixes classified into 4 similarity classes, are found. It is established the general number of basis Hadamard matrices, namely 768, which are classified into 10 similarity classes.