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vector quantity of one of the physical properties depending on the direction (deffirent values in deffirent directions), such as conductivity, risitance, etc.
It is a generalization or higher rank of matercies. For example, vector is a tensor of rank one and matercies is of rank two. Tensors is a tool to genralize many of the mathematical and physical concept. For instance, it is a main tool to study general relatvity and the geomtry of the spacetime using the metric.
This article gives a nice introduction to the subject
Tensor describe geometric relation between scalar-scalar,scalar-vector,vector-vector and even other tensors.