Maths - Inverse Vector - Martin Baker

Maths - 4 Dimentional Vector Geometry

Points and Lines from the Origin

We can use a 4 dimensional vector to represent a displacement from the origin and therefore specify a given point

Angles

In 4 dimensions rotations have 6 degrees of freedom

Areas

In 4 dimensions areas can be specified by a 6-dimentional vector.

Standards

There are a lot of choices we need to make in mathematics, for example,

Left or right handed coordinate systems.
Vector shown as row or column.
Matrix order.
Direction of x,y and z coordinates.
Euler angle order
Direction of positive angles
Choice of basis for bivectors
Etc. etc.

A lot of these choices are arbitrary as long as we are consistent about it, different authors tend to make different choices and this leads to a lot of confusion. Where standards exist I have tried to follow them (for example x3d and MathML) otherwise I have at least tried to be consistent across the site. I have documented the choices I have made on this page.

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see also:

Correspondence about this page

Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics (Fundamental Theories of Physics). This book is intended for mathematicians and physicists rather than programmers, it is very theoretical. It covers the algebra and calculus of multivectors of any dimension and is not specific to 3D modelling.

Commercial Software Shop

Where I can, I have put links to Amazon for commercial software, not directly related to the software project, but related to the subject being discussed, click on the appropriate country flag to get more details of the software or to buy it from them.

Can you help?

Please send me any improvements to here. I would appreciate ideas to make the pages more useful including error correction, ideas for new pages, improvements to wording. It helps if you quote the full URL of the page.

Terminology and Notation

Specific to this page here:

program

I am working on a project which uses these principles, if you would like to help me with this you are welcome to join in, here:

http://sourceforge.net/projects/mjbworld/

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