Medisis

All about vectors and spaces

If you are a medical doctor and reading this, you should remember that in Matric physics a vector was defined as something with magnitude and direction. This however is only part of the story.

Before I start telling you about spaces,bases and dimensions. I want you to imagine a vector is pointing in a positive x and y direction with an angle of 30 degrees (Π/6) from the x axis. The vector can be expressed as ( m*cos30 , m*sin30) This is known as the components of a vector. Now once this is realised. What would the following set of numbers be but a vector in a higher dimension (4,6,2,9,3). See thing is you don't have to stop at to or three numbers as components. This fact was discovered my mathamaticians and physicists in the mid eighteenth century. This brings me to the idea of the Euclidean vector space or n-space where n would be the number of components specified in the vector. This space is needed if the components are more than three. This is because every thing you can see exists in three dimensions. A color for instance expressed as four numbers, a red number, a blue number a yellow number and a transparency number can't exist in 3-space...

Not that difficult... If you are working in 15-space, you need some way of expressing these components in terms of one and other. This is were the idea of a base comes in. The formal mathematical definition for a base is. "The set of vectors that both span the space and are linearly independent from each other". This is a very exact way of saying that any vector in that space can be expressed as a combination of this set of vectors.

In my experience doctors like this word but I do not believe they have any idea what it means. Lets say in this application you define 10 symptoms thus you are working in 10-space, for the sake of simplicity you base is ten vectors. That base for that space has a dimensional nature of ten. For further reading on this topic "Google"