An elementwise tensor operation applies a standard scalar function to the individual elements of a tensor. For a unary scalar operator, denoted mathematically as $f: \mathbb{R} \rightarrow \mathbb{R}$, the function maps each real number in the tensor to another real number independently. For a binary scalar operator, denoted as $f: \mathbb{R}, \mathbb{R} \rightarrow \mathbb{R}$, the operation maps pairs of real numbers to a single real number. When a binary operator is applied to two tensors of identical shape—whether they are vectors, matrices, or higher-order tensors—the function evaluates each pair of corresponding elements to produce a new tensor that has the exact same shape as its operands.