Tensors are one of the most widely used data structures in modern Machine
Learning applications. Although they provide a flexible way of storing and
accessing data, they often expose too many low-level details that may result in
error prone code that is difficult to maintain and extend. Abstracting
low-level functionalities into high-level operators in the form of a query
language is a task in which the Data Management community has extensive
experience. It is thus important to understand how such an experience can be
applied in the design of useful languages for tensor manipulation. In this
short paper we study a matrix and a tensor query language that have been
recently proposed in the database literature. We show, by using examples, how
these proposals are in line with the practical interest in rethinking tensor
abstractions. On the technical side, we compare the two languages in terms of
operators that naturally arise in Machine Learning pipelines, such as
convolution, matrix-inverse, and Einstein summation. We hope our results to
provide a theoretical kick-o for the discussion on the design of core
declarative query languages for tensors.