Particle coordinates and discrete molecular description: a geometric point of view on a twofold dimensionality environment

In the present study a specific kind of widespread mathematical objects: descriptor matrices are defined and studied. These are matrices connected with several problems concerning many fields of interest in theoretical chemistry, classical and quantum mechanics, or quantitative structure-properties relations. The twofold dimensionality structure of descriptor matrices is analyzed and the properties of descriptor matrices are also disclosed with respect origin shifts and rotations. A tensor to study schematically the three dimensional nature of many particle structures, the characteristic form tensor is defined. The construction of similarity matrices from descriptor matrices and the connection with quantum similarity are finally discussed.