Hands-On Mathematics for Deep Learning

Comparing scalars and vectors

Scalars are regular numbers, such as 7, 82, and 93,454. They only have a magnitude and are used to represent time, speed, distance, length, mass, work, power, area, volume, and so on.

Vectors, on the other hand, have magnitude and direction in many dimensions. We use vectors to represent velocity, acceleration, displacement, force, and momentum. We write vectors in bold—such as a instead of a—and they are usually an array of multiple numbers, with each number in this array being an element of the vector.

We denote this as follows:

Here, shows the vector is in n-dimensional real space, which results from taking ...