Describing the topological properties by a template is a powerful technique to classify chaotic attractors. Most of the time, reduced template are used but direct templates -in which all mechanisms (torsions, branch permutation, etc.) identified in the attractor are explicitely described without any simplification -are of a great interest to have a better description of the subtleties of the dynamics. We here introduce two additional conventions to represent in an unique way the reduced

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... from a given linking matrix. Then, we propose an addition law for linking matrices which allows to manipulate (combine) different mechanisms. Direct template can thus be described by using a series of linking matrices. In the other hand, we show how to analytically build the linking matrix associated with an attractor which is the image under an inversion symmetry of an attractor whose linking matrix is known.