Its domain is the matrix a of det, and the determinant can also be regarded as a generalization of the concept of directed area or volume in general Euclidean space. In other words, in N-dimensional Euclidean space, determinant describes the influence of a linear transformation on "volume".
Determinant is a square matrix composed of several numbers, and its value is the algebraic sum of all different products, which can be obtained by the following methods. When obtaining each meta-factor, take out one meta-factor from each row in turn, and each meta-factor needs to be taken out from a different column.
As a multiplier, the sign of the product is exactly negative, depending on whether the number of transpositions required to restore the exponential order of each multiplication series to the natural order is even or odd.
Whether in linear algebra, polynomial theory or calculus (such as substitution method and integral method), determinant, as a basic mathematical tool, has important applications.