Common basic knowledge of linear algebra

1. Determinant1.1 Second-order determinant

1.2 third-order determinant

1.3 Number of reverse order

1.4 N-Step determinant

2. The nature of the determinant

Property 1 The determinant is equal to its transpose determinant.
Property 2 swaps the determinant of two rows (columns), determinant.
Property 3 The determinant of a row (column) in which all elements are multiplied by the same multiplier K, equals the number k multiplied by this determinant.
Property 4 Determinant If there are two rows (column) elements proportional, then this determinant is zero.

The determinant row and column have the same status, the nature of the establishment of the line is also established.

The commonly used methods of calculating determinant are: (1) using the definition, (2) using the property to make the determinant into the upper triangular determinant, so as to calculate the determinant value.

3. Solving equation groups3.1 carat The law of the Silent

Theorem 4 If the coefficient determinant of a linear equation group is not equal to zero, then the linear equation group must have a solution, and the solution is unique.

Theorem 4′ If a linear equation group has no solution or has two different solutions, the determinant of its coefficients must be 0.

4. Matrix

4.1 Special matrices

4.2 Matrix and Linear transformations

4.3 operation of the matrixaddition of the 4.3.1 matrix

4.3.2 number multiplied by the matrix

4.3.3 Matrix and matrix multiplication

Transpose of the 4.3.4 matrix

determinant of 4.3.5 phalanx

Common basic knowledge of linear algebra