The plane equation in the determinant form above represents the plane passing through three points in space (x 1, y 1, z 1), (x2, y2, z2), (x3, y3, z3), and can also be written as the plane equation of the fourth-order determinant as follows:

In mathematics, determinant is a function of matrix A whose domain is det, and its value is scalar, which is denoted as det(A) or | A |. Whether in linear algebra, polynomial theory or calculus (such as substitution integral method), determinant, as a basic mathematical tool, has important applications.

Determinant can 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".

Extended data

Mathematical definition of determinant

N-order determinant

Is made up of n arranged in an n-order square matrix? The number aiji (I, j = 1, 2, ..., n), whose value is n! The sum of projects.

Where k 1, k2, ..., kn are exchanged by the sequence 1, 2, ..., n represents k times, and σ represents k 1, k2, ..., kn.

References:

Baidu encyclopedia determinant