Linear Algebra For Machine Learning: A Simple Guide In 2021


In recent years, computer vision, robotics, machine learning, and data science have been key areas that have contributed to major advances in technology. In machine learning, algorithms are trained to find patterns and correlations in large datasets and make the best decisions and predictions based on that analysis. Linear algebra for machine learning applications improve with use and become more accurate. The more data they have access to, the better the algorithm, the more accurate the decisions and predictions. Applications of machine learning are all around us. Digital assistance “Alexa” search the internet and play music in response to our voice commands. We often see websites recommend products based on what we searched, bought, watched, or listened over the internet. 

  1. What is Linear Algebra?
  2. Minimum Linear Algebra for Machine Learning
  3. Linear Algebra for Machine Learning Examples
  4. Reasons to Improve Your Linear Algebra

1. What is Linear Algebra?

Linear Algebra is a key branch of mathematics. It a branch of mathematics that is concerned with mathematical structures used for the operations of addition and scalar multiplication, and that includes the theory of systems of linear equations, matrices, determinants, vector spaces, and linear transformations. It is also essential for understanding Machine Learning algorithms.

2. Minimum Linear Algebra for Machine Learning

Linear Algebra helps in mixing science, technology, finance & accounts, and commerce altogether. One must have a solid background in linear algebra to develop and work in the Machine Learning environment. 

Below are some linear Algebra for machine learning concepts which are mostly used in Machine Learning implementation:

  • Scalar: It is a physical quantity described using a single element. It has only magnitude and not direction. Basically, a scalar is just a single number.
  • Vector: It is a geometric object having both magnitude and direction. It is an ordered number array and is always in a row or column. A Vector has just one index, which can refer to a particular value within the Vector.
  • Matrix: An ordered 2D array of numbers, symbols, or expressions arranged in rows and columns. It has two indices. The first index points to the row, and the second index points to the column. A Matrix can have multiple numbers of rows, and columns.
  • Transpose: The transpose of a matrix generates a new matrix in which the rows become columns and columns become rows of the original matrix.
  • Inverse: The inverse of a matrix is the matrix, when multiplied with the original matrix, gives the Identity matrix as the product. If m is a matrix and n is the inverse matrix of m, then m*n = I, representing the Identity matrix.
  • Tensor: It is an algebraic object representing a linear mapping of algebraic objects from one set to another. It is actually a 3D array of numbers with a variable number of axes arranged on a regular grid. A tensor has three indices, the first index points to the row, the second index points to the column, and the third index points to the axis.

3. Linear Algebra for Machine Learning Examples

  • Data sets and data files: A Machine learning dataset is defined as the collection of data that is needed to train the model and make predictions. 
  • Images and photographs: Image classification has become one of the key pilot use cases for demonstrating machine learning. Deep Learning methods have displaced classical methods and are achieving state-of-the-art results for the problem of automatically generating descriptions, called “captions,” for images. 
  • Regularization: Regularisation is a technique used to reduce errors by fitting the function appropriately on the given training set and avoid overfitting.
  • Deep Learning: Deep learning is a subset of machine learning in which multi-layered neural networks are modelled to work like the human brain ‘learn’ from large amounts of data.
  • Linear Regression: Linear Regression in Machine Learning is one of the most popular machine learning algorithms. 
  • One Hot Encoding: It refers to splitting the column, which contains numerical categorical data, into many columns depending on the number of categories present in that column. Each column contains “0” or “1”, corresponding to which column it has been placed.
  • Principal Component Analysis: Principal Component Analysis (PCA) is an unsupervised statistical technique algorithm. PCA also serves as a tool for better data visualization of high-dimensional data. We can create a heat map to show the correlation between each component.
  • Singular value decomposition: In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix, with many useful applications in signal processing and statistics. It is a type of factorization of a matrix into a product of three matrices. The second is a diagonal matrix that has the entries on its diagonal the singular values of the original matrix.
  • Latent Semantic Analysis: LSA is an information retrieval technique that analyses and identifies the pattern in an unstructured collection of text and the relationship between them.

4. Reasons to Improve Your Linear Algebra

The reason why learning linear algebra is of paramount importance to excel in machine learning are as follows:-

  1. Machine learning involves a significant amount of data, and thus, knowing how to read and write the vector notations and matrix representations of sets becomes imperative. Algorithms of data analysis can be very easily explained by using these notations. It allows one to read algorithms given in textbooks, elucidate and execute new functions and briefly describe those learnings to users. Languages such as Python deploy use linear algebra symbols, and an understanding of the same will give one systematic view of machine learning algorithms. Decision trees, linear regression, logistic regression, support vector machines, and ensemble methods fall under supervised learning algorithms. Linear Algebra will facilitate a deeper understanding of the ML project, which provides the flexibility to customize any parameters involved.
  2. Data analysis and statistics are the primary domain of machine learning. It plays a role in the interpretation of data. Linear algebra has been called the “mathematics of data” and is an integral part of numerous mathematics branches, including statistics. Consider a domain such as healthcare. Analytics are used for diagnostics, insurance, and health history, predicting future disease regression, and graphical representations amidst other features.
  3. ML projects mostly include audio, video, and images together with graphical parts such as edge detection. Classifiers are used to place data sets and train them category-wise. They are used to detect errors from trained data. Here linear algebra is used as an engine to run large chunks of data.


Machine Learning is the new buzzword and Artificial Intelligence, Data Analytics, Data Mining for new age professionals. Still, to master it, you must know the math behind it and learn some of the Linear Algebra for machine learning concepts that are used in any ML or Deep Learning project.

There are no right or wrong ways of learning AI and ML technologies – the more, the better! These valuable resources can be the starting point for your journey on how to learn Artificial Intelligence and Machine Learning. Do pursuing AI and ML interest you? If you want to step into the world of emerging tech, you can accelerate your career with this Machine Learning And AI Courses by Jigsaw Academy.


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