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".
The solution of claw determinant is: multiply the second column by a coefficient, add it to the first column, make the first column zero except the first element, and then expand it in the first column to get the result.
Claw determinant: Multiply each column by a corresponding multiple and add it to 1 column, and turn all rows below 1 into 0 to get the triangle above, and then multiply it by the main diagonal element.
An E-order Vandermonde determinant is determined by the numbers C, C, …, C, and its 1 rows are all 1, which can also be regarded as the 0 th power of the numbers C, C, …, C, and its second row is C, C, …, C (1 power), which is its first power.
Characteristics of claw determinant:
1, characteristic 1: arrangement structure
The arrangement structure of claw determinant is claw-shaped, which consists of a central element and symmetry element on both sides. This arrangement is rare in the matrix, so it is unique.
2. Feature 2: Determinant value
The determinant value of claw determinant can be calculated by block matrix method. Because of its special arrangement structure, the calculation is relatively simple and intuitive, and it is suitable for solving some specific problems.
3. Feature 3: Zero element
In the claw determinant, all elements except the central element are zero. This means that many elements can be ignored when calculating claw determinant, which simplifies the operation steps.