First of all, the main difference between linear algebra and calculus lies in the research object and method. Calculus mainly studies the concepts of limit, derivative and integral of functions and their applications in solving practical problems. Linear algebra mainly studies the properties of vectors and vector spaces, as well as linear transformation and the solution of linear equations. The method of calculus mainly studies the changing law of functions through limits and derivatives, while the method of linear algebra studies the properties of vectors and vector spaces through matrix operations.
Secondly, the main difference between linear algebra and probability theory and mathematical statistics lies in the research content and application. Probability theory and mathematical statistics mainly study the regularity of random phenomena and how to use these regularity to make predictions and decisions. Linear algebra mainly studies the properties of vectors and vector spaces, as well as linear transformation and the solution of linear equations. Although some concepts and methods of linear algebra are also applied in probability theory and statistics, the main application fields are different.
Generally speaking, linear algebra is a unique mathematical field, which has its own unique research objects and methods, which are obviously different from other mathematical fields. At the same time, linear algebra is also the foundation of many other mathematical fields, such as calculus, probability theory, statistics and so on.