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# Linear Algebra in Machine Learning

[Duke University]

### - Overview

Linear algebra (LA) is a branch of mathematics that is essential to machine learning (ML). It is the math of arrays, which are also known as vectors, matrices, and tensors. LA is used to represent data and perform computations in ML models. It also forms the foundation of ML algorithms, allowing operations like matrix multiplication, which are important for model training and prediction.

Linear algebra (LA) is the study of vectors, which are ordered lists of numbers. Vectors are the most fundamental mathematical object in ML. They are used to represent attributes of entities, such as age, sex, and test scores.

For example, a black and white image can be represented as a vector by associating the pixels with numbers zero or one to indicate black or white.

Some recommend linear algebra as a prerequisite before a data scientist starts to apply the concept of ML.

### - Linear Algebra for Machine Learning

Linear algebra (LA) is a pillar of machine learning (ML). You cannot develop a deep understanding and application of ML without it. It is very important to have sufficient knowledge of a few LA concepts if you are looking to understand the underlying concepts behind ML. If you don’t know the math behind these advanced ML algorithms, you can’t wish to develop a mastery over them.

Areas of mathematics such as statistics and calculus require prior knowledge of LA, which will help you understand ML in depth. Many ML experts may be of the opinion that LA helps to some extent, but it definitely improves one’s math skills and intuition in ML.

Linear Algebra (LA) is a branch of mathematics that deals with linear equations and linear functions which are represented through matrices and vectors. In simpler words, LA helps you understand geometric terms such as planes, in higher dimensions, and perform mathematical operations on them.

By definition, algebra deals primarily with scalars (one-dimensional entities), but LA has vectors and matrices (entities which possess two or more dimensional components) to deal with linear equations and functions. LA can also be called as the extended version of algebra.

Here are a few concepts of LA that you need to learn about for knowing how ML works. They are:

• Vectors and Matrix
• Symmetric Matrix
• Eigenvalues and Eigenvector
• Principal Component Analysis (PCA)
• One-Hot Encoding
• Linear Regression
• Regularization
• Singular-Value Decomposition
• Latent Semantic Analysis
• Recommender Systems

[Switzerland - Civil Engineering Discoveries]

### - Linear Algebra for Data Science and Machine Learning

Linear algebra (LA) is the bedrock of data science. Knowing LA boosts your ability to understand data science algorithms.

Linear Algebra (LA) is a continuous form of mathematics and is applied throughout science and engineering because it allows you to model natural phenomena and to compute them efficiently. Because it is a form of continuous and not discrete mathematics, a lot of computer scientists don’t have a lot of experience with it.

LA is also central to almost all areas of mathematics like geometry and functional analysis. Its concepts are a crucial prerequisite for understanding the theory behind Machine Learning, especially if you are working with Deep Learning Algorithms.

You don’t need to understand LA before getting started with ML, but at some point, you may want to gain a better understanding of how the different ML algorithms really work under the hood.

This will help you to make better decisions during a ML system’s development. So if you really want to be a professional in this field, you will have to master the parts of Linear Algebra that are important for Machine Learning.

In linear algebra (LA), data is represented by linear equations, which are presented in the form of matrices and vectors. Therefore, you are mostly dealing with matrices and vectors rather than with scalars. When you have the right libraries, like Numpy, at your disposal, you can compute complex matrix multiplication very easily with just a few lines of code.

### - Examples of Linear Algebra in Machine Learning

Here are 10 examples of linear algebra (LA) in ML:

• Dataset and Data Files
• Images and Photographs
• One-Hot Encoding
• Linear Regression
• Regularization
• Principal Component Analysis
• Singular-Value Decomposition
• Latent Semantic Analysis
• Recommender Systems
• Deep Learning

[More to come ...]