# Matrices, Vectors & Algebra¶

The rw::math namespace includes many math types for representing different types of vectors. Math types in RobWork are based on Eigen 3.

## Notation¶

In general a diagonal notation form will be used to describe the relation of vectors, rotation matrices, homogeneous transform, velocity screw, and so on.

Expression

Description

$${}^{a}{\mathbf{P}}$$

Vector P seen in frame a

$${}^{a}{b}_{\mathbf{P}}$$

Translation of frame b seen in frame a

$${}^{a}{b}_{\mathbf{R}}$$

Rotation of frame b seen in frame a

$${}^{a}{b}_{\mathbf{T}}$$

Homogeneous transform of frame b seen in frame a

$${}^{a}_{b}{\mathbf{T}_v}^{c}_{d}$$

Velocity transform that transforms the reference frame from
b to a and the velocity reference point from c to d

$${}^{a}_{b}{\mathbf{T}_f}^{c}_{d}$$

Force transform that transforms the reference frame from
b to a and the force reference point from c to d

$${}^{a}{b}_{\mathbf{J}}$$

A Jacobian matrix defined from reference frame a to frame b

When coordinate frames are visualized the axes are illustrated with the colors RGB, such that Red(x-axis), Green(y-axis) and Blue(z-axis).

## Jacobians¶

Note

Documentation is being written…

## Polynomials¶

Note

Documentation is being written…

## Singular Value Decomposition (SVD)¶

Note

Documentation is being written…

## Linear Algebra¶

Note

Documentation is being written…

## Polynomials¶

Note

Documentation is being written…