vol 4: Glossary
Site map
Directory
Search this site
Home
1: About
2: Synopsis
3: Development
Next:
Previous: Glossary: Toc
... to restore theology to the mainstream of science
Vector space
Introduction
We imagine that mathematical spaces exist in an independent way, like the landscape. Often it helps to find our way around them if we introduce systems of coordinates. Cartesian coordinates enable us to give each point in Euclidean space a name. We represent the name of a point with respect to certain coordinates by a set of numbers called a vector. In one dimensional space (that is on a line) each point is represented by just one number, its distance from an arbitrary point called the origin, whose coordinate is 0. A point one unit to the right of the origin is called 1, a point two units to the left, -2 and so on.
Points in two dimensional space ("the cartesian plane") are specified by two numbers, and so on. Points in a space with a countable number of dimensions are specified by ordered sets or vectors with a countable number of elements or components. As the number of dimensions of space increases, the amount of information encoded in each point of the space also increases. Given enough dimensions, we can encode any ordered set as a single point.
Axioms
Click on an "Amazon" link in the booklist at the foot of the page to buy the book, see more details or search for similar items
Related sites:
Concordat Watch
Revealing Vatican attempts to propagate its religion by international treaty
