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| index | algebra | geometry | calculus | graph theory | statistics | principles | standards |
| index | books | notation | program |
| notation | meaning |
|---|---|
| [M] | matrix |
| [M]t | transpose of matrix (swap rows & columns) |
| [M]-1 | inverse of matrix |
| [I] | identity matrix (ones on leading diagonal, otherwise zeros) |
The individual elements of the matrix are numbered as follows,
| m00 | m01 | m02 | … | m0n |
| m10 | m11 | m12 | … | m1n |
| m20 | m21 | m22 | … | m2n |
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| mp0 | mp1 | mp2 | … | mpn |
The first subscript represents the row, the second subscript represents the column.
| notation | meaning | basis | Alternative |
|---|---|---|---|
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direct sum or Kronecker sum depending on context | ||
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direct product or Kronecker product depending on context | ||
| ^ | exterior algebra | ||
| ^k | exterior algebra kth blade | ||
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scalar or real depending on context (see below) | e0 | |
| ² |
2 dimensional vector | e1,e2 | |
| ³ |
3 dimensional vector | e1,e2,e3 | |
| n |
n dimensional vector | e1…en | |
| ^²² |
bivector based on 2D algebra | e12 | |
| ^²³ |
bivector based on 3D algebra | e12,e31,e23 | |
| C | complex numbers | |
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| H | quaternions | ³ |
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| O | octonions | 7 |
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a A |
a is an element of the set A | ||
I have used the term 'scalar' interchangeably with the term 'real', that is, a continuous value that can be represented by a single number.
Strictly speaking the term 'scalar' should be reserved for a quantity that is used to scale a vector, that is change its magnitude without changing its direction, or in other words a scalar is the ratio of parallel vectors.
For instance I should not really call energy a scalar because there are no vectors involved.
I apologise for my lack of mathematical rigor here, its just that the word scalar seems to better express that it is not a vector and its less likely to cause confusion with the real part of a complex number. Also this (mis?)usage is quite common in the computer world.
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| see also: | |
| Correspondence about this page | |
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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. |
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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. |
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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. |
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progam 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: |
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This site may have errors. Don't use for critical systems.
Copyright (c) 1998-2008 Martin John Baker - All rights reserved.
