Linear algebra is a versatile tool which has various applications outside of general mathematics. It is a branch of mathematics that describes coordinates and interactions of planes in higher dimensions and allows one to perform a wide variety of operations on them. It is usually about working on a system of linear equations, being of paramount significance to understand complex processes in machine learning.
The notation is essential: Machine learning involves a significant amount of data and thus knowing how to read and write the vector notations and matrix representations of sets become imperative. It gives you the flexibility to illustrate operations performed on data accurately with individually available operators. 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.
Linear algebra arithmetic: It is now evident that knowing just the notations wouldn't help much, they have to be complemented with the underlying linear algebra arithmetic operations such as addition, subtraction, multiplication, inverse, the transpose of matrices, scalars and vectors. Beginners find it daunting to go about matrix multiplication and tensor multiplication which are not so direct and perceivable. Many of these operations are present in new linear algebra libraries via API calls. Thus knowing linear algebra will help one immensely in their stint with machine learning.
For its applications in statistics: Data analysis and statistics is a primary domain of machine learning. It plays its role in the interpretation of data. Linear algebra has been called as the "mathematics of data" and is an integral part of numerous branches of mathematics including statistics. Consider a domain such as healthcare. Analytics are used for diagnostics, insurance, and health history, predicting future diseases regression and graphical representations amidst other features.
For processing graphics in machine learning: ML projects mostly includes items such as 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. It instills a specific matrix decomposition technique for the project to handle and process the data. L-U decomposition is used to split a square matrix into an upper-triangular and lower-triangular matrix whereas Q-R decomposition is used for the order of n*m matrices.
Method of least squares: There are many instances in linear algebra when there are more equations than there are unknown variables. It becomes difficult as no single solution exists for the set. Such problems can be solved using minimization of square error, called least squares and linear algebra is a versatile method for this. Linear least squares have its applications in matrix factorization. It is known for its dynamic part in linear regression models.
Linear algebra is exciting and fun to learn. It is practical, efficient and straightforward and shall boosts one's machine learning and data analytical skills. Nowadays, there are many machine learning courses in India which offer preliminary knowledge of linear algebra. Doing such courses dramatically improves one's mathematical and thinking skills and pushes us one step forward. It is undeniably a sturdy branch of machine learning. I hope that this creates a spark in you to delve into it and refine your knowledge of machine learning.