Linear algebra is a branch in mathematics that deals with objects and operations in what is called -dimensional space. Most students are already familiar with 1, 2 and 3-dimensional spaces from elementary algebra. 1-dimensional space can be visualized as a number line as shown in Figure 1-1. The only objects are points which can be represented by a single numerical values.
Figure 1-1.
Number Line
2-dimensional space is a flat plane and consists of primitive objects such as points and lines. Individual objects are combined to form more complicated ones such as the parallelogram in Figure 1-2. 3-dimensional space consists of points, lines, and planes. Once again, objects such as a parallelpiped (pronounced parallel-pipe-ed) can be formed from more primitive objects. Operations on objects range from finding the distance between two points to rotations and translations of the object.
Object could not be loaded.
Figure 1-2.
Parallelogram in 2D Space
Object could not be loaded.
Figure 1-3.
Parallelpiped in 3D Space