Within the curriculum framework of Chinese universities, linear algebra is usually a linear algebra course for non-mathematical science and engineering majors, while advanced algebra is a substitute course for mathematics majors. Linear algebra focuses on determinant, matrix and its transformation, linear equations, quadratic form and other relatively specific concepts, and attaches importance to calculation; Higher algebra in mathematics department may focus on linear space and linear transformation in general fields, and then emphasize the relationship between matrix and linear transformation. Some respondents mentioned that the senior generation can talk about polynomials, which is actually very understandable. All polynomials form a linear space, and derivatives or integrals are linear transformations on it, which naturally belongs to the discussion of line generation. The determinant itself is a multivariate polynomial; Discriminant, resultant and so on are also the places where polynomial theory and matrix theory connect. Then the basic symmetric polynomial of the eigenvalue gives the coefficients of the eigenvalue polynomial, and so on.
Finally, in the eyes of some mathematicians, linear algebra studies linear structure, and linear structure is far more than linear space, so they will think that category theory, a large block of commutative algebra (such as the finite generating module structure theorem on PID) and so on also belong to "linear algebra". But don't worry, I haven't seen anyone who teaches undergraduate line generation according to this standard-oh, I heard that Zhang did talk about PID theory in online substitute class.