Why should one learn linear algebra?

It is important to build linear algebra forms for an important learning segment for ML or Machine learning. Statistics and calculus are areas of mathematics requiring linear algebra knowledge. The majority of Machine Learning experts think that linear algebra is important to some extent. However, linear algebra improves intuition and math skills for sure. You can learn an online linear algebra course for credit.

You should get acquainted with linear algebra and its preliminaries for several reasons. Some of the most significant reasons are as follows.

Linear algebra 

Linear algebra is that branch of mathematics that deals with linear functions and linear equations represented with vectors and matrices. In other words, linear algebra helps a person understand certain geometric terms, such as higher dimensions and planes, and perform other mathematical operations on planes and dimensions.

According to the definition, algebra is the branch that deals with one-dimensional entities, such as scalars. But linear algebra deals with matrices and vectors that are two or more dimensional entities. Linear algebra deals with matrices and vectors to deal with linear functions and linear equations. Linear algebra can also be known as the extended version of algebra.

  • Linear algebra is the elementary unit for machine learning

Calculus precedes linear algebra when it comes to learning advanced math. Integral calculus and differential calculus help students learn many things without restrictions and differentiation and integration skills. It also sets a base for multi-dimensional and vector configurations, such as tensors. This is known as Matrix Calculus. 

Linear algebra is the elementary unit for machine learning. Knowing the concepts will help you to learn all the areas, such as systems of linear functions. This is the addition of some advanced topics, such as the simplex method and vector in space. Such concepts with the base are improved if a person gives his time and attention to learning machine learning and linear algebra.

  • The machine learning intuition

Learning linear algebra is necessary as it helps to improve your intuition for machine learning. This gives you enhanced perspectives. Linear algebra is all about matrices and vectors that can help you think more idealistic and broader. You are more likely to use more parameters in machine learning, visualize things, use more matrices and operations, come with a different graph, or apply better and unique codes. There are numerous possibilities when it comes to linear algebra. 

For example, you can consider a machine learning project in healthcare. Use cases can be used for preventive care, insurance, diagnostics, and patient history. Although datasets are available, the goal of making a machine learning model is certain, such as graphical depictions, regression, test data, training, and data exploration. Learn about  Distance Calculus.

  • Linear algebra helps in building better machine learning algorithms.

A person should learn linear algebra because linear algebra can help in developing popular and important Machine learning algorithms, such as Unsupervised learning and Supervised learning from scratch. Ensemble methods, support vector machines, logistic regression, linear regression, and decision trees are some things that fall under the category of supervised learning algorithms.

On the other side, single value decomposition, component analysis, and clustering are included in unsupervised learning algorithms. Linear algebra helps in giving a deeper and detailed learning of machine learning projects that give flexibility to the parameters. This is beneficial as it leads to using the resources to the fullest. 

  • Linear algebra helps to improve one’s grip on statistics

Statistics are important to assimilate and organize the data in machine learning. Linear algebra serves as a prerequisite as it helps to give the best understanding of the statistical concepts. Operations, methods, and notions in linear algebra help use advanced topics such as multivariate analysis in statistics. 

For example, let us have an example of a doctor with all the required patient data, including weight, height, heart rate, and blood pressure. There will be multiple variables in the data. Let us think that more weight is directly proportional to higher blood pressure. This is an example of linear relation in which an increase in a variable causes an increase in the other variable. 

Lets us think that you want to perform an analysis on multivariate regression in statistical software, i.e. Stata; you will have to use mvreg and manova commands. The mvreg command gets the parameters, such as estimation parameters. The manova command is used to get the statistically compatible equations. The statistical result that is obtained acts as a linear function, and it is converted into a matrix later to work in machine learning.

  • Linear algebra for processing graphics in machine learning

The machine learning projects involve the objects, such as images, videos, audio and other graphical interpretations, including edge detection. Machine learning algorithms make the classifiers select some part of the database and train them according to a certain category. The classifiers also try to remove errors from the trained data. This is about getting the linear algebra into a picture. This helps to compute complex and large data. 

Linear algebra involves matrix decomposition techniques for better handling and processing of data. Q-R and L-U decomposition are the most popular methods used for the same purpose.

L-U decomposition method is used to split the square matrix into two matrices. These are called lower-triangle matrix and upper-triangle matrix. These are sub-matrices. These are obtained according to the programming language being used. 

Q-R decomposition is used for non-square matrices. The order of non-square matrices is n x m. Q-R decomposition simplifies the graphical needs and uses the resources to the fullest to get an optimal graph. 

The takeaway

For a machine learning beginner, linear algebra might be challenging to learn. However, linear algebra has a wide range of concepts that a person needs to learn. Certain concepts, such as the system of linear equations and linear functions, might be challenging for people to learn.

It all requires a bit of effort and practice to grasp the concepts. Hard work and passion will make this challenging task no more challenging. There are multiple-fold benefits of learning linear algebra. It improves a person’s programming and math skills and helps explore the broader side of machine learning.

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Christophe Rude

Christophe Rude

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