Tensor slicing is a technique used to select a range of elements, such as a contiguous range of rows, along one or more axes of a tensor. For example, programmatically applying a slice like $$[1:3]$$ to a matrix selects its second and third rows.

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Like elements in standard Python lists, the individual elements within a tensor can be accessed using indexing. Tensor indexing is zero-based, meaning the first element along any given axis is located at index $$0$$. It is important to contrast this programmatic convention with formal linear algebra, where vectors typically utilize one-based indexing (starting at subscript $$1$$).

Tensor Indexing

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Tensors allow for negative indexing, which is a method used to select elements based on their relative distance from the end of an axis. For instance, using an index of $$-1$$ retrieves the final element along that particular dimension, while $$-2$$ retrieves the second-to-last element.

Negative Tensor Indexing

When a single index or slice is provided for a $$k^{	extrm{th}}$$-order tensor (where $$k > 1$$), the selection operation defaults to being applied along axis $$0$$. For example, applying the index [-1] to a matrix returns its last row, while the slice [1:3] returns its second and third rows.

Default Axis for Tensor Indexing

Specific elements or contiguous ranges within a tensor can be modified in-place by specifying their indices and assigning new values. By positioning indexing or slicing operations on the left-hand side of an assignment operator, data can be written directly to those specific locations within the tensor.

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