Tensorrekening

Tensorrekening is a branch of mathematics that deals with tensors. Tensors are mathematical objects that generalize scalars, vectors, and matrices. A scalar is a rank-0 tensor, a vector is a rank-1 tensor, and a matrix is a rank-2 tensor. Tensors can have higher ranks, meaning they can represent more complex relationships between mathematical objects.

The core idea behind tensorrekening is to provide a framework for describing physical and geometric phenomena in a way that is independent of the coordinate system used. This means that the laws of physics, for example, can be expressed in a form that remains the same regardless of whether you are describing them in Cartesian coordinates, polar coordinates, or any other coordinate system. This invariance is a fundamental property of tensors.

Key concepts in tensorrekening include tensor contraction, tensor product, and the transformation rules that tensors obey when changing coordinate systems. These rules ensure that the physical quantities represented by tensors remain consistent. Tensorrekening has important applications in various fields, including general relativity, fluid dynamics, elasticity, and machine learning, where it is used to represent and manipulate multi-dimensional data.