tenzory

Tenzory are mathematical objects that generalize scalars, vectors, and matrices. A scalar is a rank-0 tenzor, a vector is a rank-1 tenzor, and a matrix is a rank-2 tenzor. Tenzory can have higher ranks, meaning they have more indices. For instance, a rank-3 tenzor can be thought of as a cube of numbers.

The defining characteristic of a tenzor is how its components transform under a change of coordinates. This transformation rule is crucial for tenzory to represent physical quantities that are independent of the observer's coordinate system. For example, stress and strain in materials are often described using tenzory.

In physics, tenzory are used extensively in areas like general relativity, where the metric tenzor describes the curvature of spacetime, and in fluid dynamics. In computer science, particularly in machine learning, tenzory have become fundamental data structures. Libraries like TensorFlow and PyTorch are named after these objects, highlighting their importance in representing and manipulating multi-dimensional data for neural networks and other deep learning models. Understanding tenzory is key to grasping many advanced concepts in both theoretical physics and modern data science.