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What are the Applications of Linear Algebra?


Whenever we talk about the field of data science in general or even the specific areas of it that include natural process, machine learning, and computer vision, we never consider linear algebra in it. The reason behind overlooking linear algebra applications is that all the tools that are being used today to implement data science algorithms are doing an excellent job in hiding the underlying math that makes everything true. Another reason why the majority of people avoid getting into linear algebra is that it is difficult or very hard to understand.

Although these facts might be true and yes understanding linear algebra applications is a little tricky but it is also true that getting familiar with linear algebra is an essential skill for data scientists and computer engineers. So no matter how much you try to ignore linear algebra, you can’t entirely free yourself from it. And that is why today, we are here with the different linear algebra applications that we think everyone should know.

 Linear Algebra Applications:

Linear algebra applications is known to be the core of many data science algorithms and here we shall be discussing the three applications of linear algebra in three data science fields.

Machine Learning:

Everyone is familiar with the term Machine Learning and without any doubt, it is the most known application of artificial intelligence (AI). Now the main purpose of machine learning is to give out different systems all the power to learn and improve automatically from experience. And that too without being explicitly programmed to do so. Machine learning functions by building all such programs that have access to data (either constant or updated). So as to analyze, find patterns, and then finally learn from them. As soon as the program is able to find the relationships in the data, it applied all this knowledge to new sets of data.

Now linear algebra has a variety of applications in machine learning. It includes loss functions, regularization, support vector classification, and more. However, we will talk about the most important one, that is, loss of function.

Loss Function:

Like we have explained earlier, machine learning works in a pattern. First, they collect data, then analyze it, and then build a model using different approaches. And then, based on the results, they are able to predict future data queries. Although, this all is done in a mannerly order, how can we measure the accuracy of our prediction model?

Well, this is done using the loss function. The loss function is a method where you can evaluate how accurate the prediction models are. Will they be performing well with the new datasets? If the model is totally off then your loss function will output a higher number. And if there were a good one then the loss function is going to output a lower amount

Computer Visions:

This is the second one from linear algebra applications It is a field of artificial intelligence that is used to train computers to interpret and understand the visual world more easily. Now, this is done using images, videos, and deep learning models. Now doing this way, it will allow algorithms to identify and classify objects more accurately and make them capable of seeing visual data. In computer vision, linear algebra is used in different applications which include image recognition and some image processing techniques that include image convolution and image representation as tensors. And we mostly call these tensors vectors in linear algebra.

Image Convolution:

This is also one of the  Linear Algebra Applications Convolutions can be considered as one of the fundamental building blocks in computer vision in general. And is termed as image processing in particular. If put in simpler words, convolution is an element-wise multiplication of two matrices that are followed by a sum. Images are represented by a multi-dimensional array in image processing applications. It is represented that way because it has rows and columns that represent the pixels of the image as well as other dimensions for the color data

Natural Language Processing:

Natural Language Processing is known well to be a branch of artificial intelligence that fairly deals with the interaction that is made between computers and humans using the natural language. This natural language is most often, English. The NLP contains different Linear Algebra applications like ChatBots, speech recognition, and text analysis. A very good example that can fit here to make you understand what NLP is, is Grammarly. We all use Grammarly, right? But do you actually know how it’s built? Well, Grammarly is built based on the concepts of the NLP.

Word Embedding:

The computers are not able to understand text data ever and that is why to perform any NLP techniques on text, we need to represent the test data numerically. And this is the part where algebra comes in. Word embedding is a type of word representation that allows words having a similar meaning to be understood by machine learning algorithms.


As you can see linear algebra applications are a very important concept but a little hard to understand. Though it is a little tricky, that doesn’t give us an excuse to not understand what it is and where and how to use it. So, if you wish to understand the applications of linear algebra then now is the time to do it. Whether you decide to enroll in a Free Online course with Certificates and study at your ease and pace or enroll in a linear algebra course where you have to follow a proper schedule. Read this article, stay home, keep yourself safe and healthy, and never stop learning