Scalars and Vectors
- [US Air Force Academy]
- Overview
In linear algebra, scalars are real numbers that relate to vectors through scalar multiplication. Scalar multiplication is the process of multiplying a vector by a number to produce another vector. The term "scalar" comes from the idea that a scalar scales vectors.
Vectors and scalars are two types of quantities used in physics and math. Scalars are quantities that only have magnitude, or size. Vectors have both magnitude and direction.
Here are some examples of scalars and vectors:
- Scalars: Speed, distance, mass, density, pressure, volume.
- Vectors: Velocity, displacement, acceleration, force, and mass
Here are some other examples of vectors:
- 60 miles per hour north
- 50 meters north
To remember the difference between vectors and scalars, you can ask yourself if there is a direction. For example, you would say "50 meters north" for displacement, but "50 meters" for scalars.
Please refer to the following for more details:
- Wikipedia: Scalar.
- Wikipedia: Vector Space.
- Applications of Vectors
Vectors are fundamental mathematical concept that have a wide range of applications in the various fields from the physics and engineering to the computer graphics and navigation systems.
In essence, a vector represents a quantity that has both magnitude and direction.
- Vectors in Machine Learning and Programming
AI engines need data to learn and operate, but what you and I think of as meaningful data is alien to machines. Machines need to translate the data into their preferred language: mathematics. This conversion happens with the help of vectors.
What are vectors in machine learning (ML)? A vector is a mathematical representation of data with magnitude and direction. We use them to transform data into mathematics that machines can understand, process, and analyze.
In ML, data is often represented and organized using vectors. Each data point is typically represented as a vector, with each component of the vector representing a feature or attribute of the data. This vector representation allows ML algorithms to process and analyze the data effectively.
By organizing data into vectors, ML models can perform various operations on the data, such as clustering, classification, and regression. Vectors enable algorithms to leverage mathematical operations, such as calculating distances and similarities, to make predictions and learn patterns within the data.
[More to come ...]
