# Theory TENSOR-QUANTITIES

## Theory documentation:

This theory is used to represent vectors of n spatial dimensions which are physical quantities with physical dimensions, such as 'the velocity of particle p'. The theory supports arbitrary numbers of basis vector sets and hence vectors are not isomorphic to n-tuples as is the case in some textbook representations of vectors (Note: Multi-basis vector spaces are essential to many theories such as kinematics). Standard vector operations such as vector addition, scalar multiplication, and scalar or dot product are supported. Operators on vector-quantities must take into account the associated units and dimensions.

The theory now also include higher-order tensors.

## Cross Reference Report:

### Theories included by Tensor-Quantities:

```  Basic-Matrix-Algebra
Scalar-Quantities```

### Theories that include Tensor-Quantities:

`  3d-Tensor-Quantities`

### 8 classes defined:

```    Matrix-Quantity
Numeric-Matrix
Orthonormal-Basis
Tensor-Quantity
Vector-Quantity
Unit-Vec
Dyad
Numeric-Tensor```

### 17 functions defined:

```  *
+
-
Basis.Dimension
Basis.Vec
Dot
Dyad-Component
Dyad-Of-Dimensions
Spatial.Dimension
Tensor-Order
Tensor-To-Matrix
The-Dyad
The-Vector-Quantity
The-Zero-Dyad-Of-Type
The-Zero-Vector-Of-Type
Vector-Component
Vector-Quantities-Of-Dimensions```

### No instances defined.

The following constants were used from included theories:

All constants that were mentioned were defined.

This document was generated using Ontolingua.
Formatting and translation code was written by
François Gerbaux and Tom Gruber