Beyond using the len() function, a tensor's length along each of its axes can be accessed via the shape attribute. The shape attribute returns a tuple indicating these lengths. For instance, a one-dimensional tensor (a vector) returns a tuple containing just a single element representing its total length.

Accessing Tensor Shape Attribute

In deep learning programming frameworks, the formal dimensionality of a vector (its number of components) corresponds directly to the tensor's length. This programmatic length can be accessed using Python's built-in len() function.

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To prevent ambiguity, deep learning terminology makes a strict distinction between 'order' and 'dimensionality'. The 'order' of a tensor refers to its number of axes, whereas 'dimensionality' exclusively refers to the number of components or elements along a specific axis (e.g., a vector's length).

Tensor Order vs. Dimensionality

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Tensor Length via Python len() Function

A matrix is a rectangular array of numbers logically arranged in horizontal rows and vertical columns. In the context of multidimensional data arrays, a matrix is formally defined as a $$2^{\textrm{nd}}$$-order tensor, meaning it is a tensor with exactly two axes. It provides a structured mathematical format to compactly organize data and is frequently used to represent systems of linear equations.

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