What Is a Vector?
The basic mathematical definition of a vector is an object that has both magnitude and direction. In our definition, it is mostly compared with a scalar, which can be defined as an object that has only magnitude. Vectors are also defined as an element in vector space—for example, a point in space with the coordinates (x=4, y=5, z=6) is a vector. Here, we can see the vector dimensions are the geometric coordinates of a point or element in space. However, the vector dimensions can also represent any quantity or property of some element or object in addition to mere geometric coordinates.
As an example, let's say that we're defining the weather at a given place using five features: temperature, humidity, precipitation, wind speed, and air pressure. The units that these would be measured in are Celsius, percentage, centimeters, kilometers per hour (km/h), and millibar (mbar), respectively. The following are the values for two places:
