Dynamics of Ice Sheets and Glaciers pp 7-16 | Cite as

# Vectors, Tensors and Their Representation

## Abstract

In mathematics, a *vector* is defined as an element of a vector space, and a vector space is a commutative (Abelian) group with a scalar multiplication. This is an abstract definition which has many possible realisations (numbers, functions, geometric objects and so on). For our purposes, it is sufficient to consider one of them, namely the geometric object of an *arrow* in the three-dimensional, Euclidian, physical space *ε*. Therefore, in our sense a vector a ∈ *ε* is an arrow which is characterised by a length and a direction. Physical quantities which can be described by such vectors are, for instance, velocity, acceleration, momentum and force. By contrast, *scalars* are simple numbers and characterise physical quantities without a direction, like mass, density, temperature etc.

## Keywords

Cross Product Scalar Multiplication Geometric Object General Tensor Index Notation## Preview

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