Basic Linear Algebra Definitions that You Hear Every Day

Do you want to start learning Machine Learning and keep hearing buzzwords related to Linear Algebra? Vector, matrix, tensor? Those are basic Linear Algebra Definitions.

Perhaps you want to learn Linear Algebra for Machine Learning and looking for a place to hit first?

In one of the previous articles, we discussed the importance of Linear Algebra in Machine Learning. Here, we introduce some of the most commonly used Linear Algebra definitions.

This article aims to accomplish the following:

• Provide the basic definitions in Linear Algebra that we hear every day while dealing with Machine Learning.
• Describe the connection between those basic concepts.
• Demonstration of the commonly used notations.

If you already know Linear Algebra and/or familiar with basic definitions, you may still find some aspects of this article useful, such as the representation of “the commonly used notations.”

Let’s get started!

Scalar and Vector

By using mathematical definition, a scalar is “an element of a field, which is used to define a vector space, usually the field of real numbers.” Simply speaking, a scalar is just a number. We usually denote a scalar with a lower case symbol, such as a.

It is worth to have a comparison between scalars and vectors. You are familiar with measures such as the velocity of a moving car and the direction of moving, which have both quantity and direction. Such elements are called vector as opposed to scalars, which have magnitude only. We denote vectors with bold symbols such as a.

Matrix

Tensor

In this tensor, each color represents a matrix and the concatenation of the matrices, form the tensor.

Conclusion

In this post, we described some of the most commonly used Linear Algebra definitions in Machine Learning. Scalar, vector, matrix, and tensor are what you hear the most. It was crucial to address them before we proceed to explain other concepts in Linear Algebra.

Originally published here, by Machine Learning Mindset.