Pronunciation: [tˈɛnsəz] (IPA) 
The word "tensors" is spelled with a soft "s" sound at the end, despite the fact that it may seem like it should end with a "z" sound. This is because it is derived from the Latin word "tensus," which ends in an "s" sound. In IPA phonetic transcription, the word is spelled /ˈtɛnsərz/, with the final sound represented by the letter "z" in English spelling actually representing the voiced "s" sound.
Tensors are mathematical objects widely used in physics and mathematics to represent and manipulate certain types of geometric data. In simple terms, tensors can be thought of as generalizations of scalars, vectors, and matrices, and they can describe more complex properties of objects and phenomena that require more than one direction or magnitude to fully characterize.
In a more technical sense, tensors are multi-dimensional arrays of numbers that transform in a specific way under rotations, stretches, and other coordinate transformations. They are defined by their rank, which corresponds to the number of indices needed to access their elements. A rank-zero tensor, also known as a scalar, is a single number that remains invariant under transformations. A rank-one tensor, or a vector, consists of a set of numbers organized in a linear array and transforms as such. A rank-two tensor, or a matrix, is a two-dimensional array of numbers, often used to describe linear transformations.
Tensors of higher ranks exist, called higher-order tensors, capable of representing more complex geometric information. They possess greater flexibility in expressing directional and structural relationships. For instance, the stress tensor in physics captures the magnitude and direction of forces acting inside a material. Similarly, in machine learning, tensors are fundamental data structures used for multi-dimensional data representation and operations in deep learning models.
The study of tensors, known as tensor calculus, provides a powerful framework for understanding and solving problems involving multi-dimensional data, geometric transformations, and physical phenomena across different scientific disciplines.
The word "tensor" was first introduced by the German mathematician and physicist Bernhard Riemann in the mid-19th century. It is derived from the Latin word "tensus", which means "stretched" or "taut". Riemann used the term to describe mathematical objects that encode how quantities change under coordinate transformations in space. The concept of tensors has since become fundamental in various branches of mathematics and physics, including differential geometry, general relativity, and vector calculus.
