#### Re: Well duh.

A 'scalar' is a single number. Think of a single point in space.

A 'vector' is a column (or row, depending on your notation) of numbers. Stretch the dot out into a line, and the values of the numbers gives the direction of the line in however many dimensions you are using. e.g. A two number vector is like coordinates on graph paper, adding a third gives height as well, and so on into harder to visualise directions.

A 'matrix' is a grid of numbers, and can be thought of as a collection of stacked vectors wrapped up in an easy to process format. It can also represent a transformation - a way of converting one vector into another. The representation is the same, just the use has changed.

All of these are also tensors, of zero, one and two dimensionality. This can be extended, so a three dimensional tensor could be displayed as a 3D grid of numbers - a stack of matrices. Then stack those into 4D, etc, until your head turns inside-out.

However, the term 'dimension' starts to get confusing, as a vector with three numbers in it can be said to represent a vector in three dimensions, but it is also a one dimensional tensor.