# Verifying Tensor Transformations

Tensors are mathematical objects that are defined by their transformation properties under a change of coordinates. This means that if a quantity transforms according to a specific set of rules involving the partial derivatives of the coordinate systems, it's considered a tensor. Based on this definition, we can verify that several expressions are indeed tensors. For example, multiplying a tensor by a scalar, adding two tensors of the same rank, and taking the outer product of two tensors all result in a new quantity that also transforms according to the correct tensor rules, thus demonstrating that these operations preserve the tensor nature of the quantities involved.

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