R The full name line is the line in the determinant.

In mathematics, determinant is an expression generated by solving linear equations. The characteristics of determinant can be summarized as multiple alternating linear forms, which makes determinant a function describing "volume" in Euclidean space.

The matrix A whose domain is nxn takes a scalar value, which is denoted as det(A) or | A |. Determinant can be regarded as a generalization of the concept of directed area or volume in general Euclidean space.

Extended data

The following is the elementary transformation of determinant:

1) Line break conversion: exchange two lines (columns).

2) Multiplication transformation: all elements of a row (column) of the determinant are multiplied by the number k together.

3) Elimination transformation: Multiply all elements in a row (column) of the determinant by a number k and add it to the corresponding elements in another row (column).

According to the basic properties of determinant, the elementary transformation of determinant has the following characteristics:

The determinant of transformation should change sign; The determinant of multiplication transformation should be changed k times; The determinant of elimination transformation remains unchanged. Elementary row transformation and elementary column transformation can be used to solve the value of determinant at the same time.