This is a mind map about the determinant. The determinant is a scalar value obtained after all the elements in a square matrix are arranged according to certain rules.
If there is a row (column) with all zero elements, the value is zero.
If there are two rows (columns) whose elements correspond to proportions, the value is zero.
If the element of a row (column) is the sum of two numbers, it can be split into the sum of two determinants
Add k times of a row (column) to another row (column), the value remains unchanged
If the elements of a certain row (column) have a common factor k, they can be mentioned outside the determinant symbol. In other words, if you use a number k to multiply the determinant, you can multiply this number to a certain row (column) of the determinant.
calculate
Level 4 and above
fully expanded
reverse number
The positive or negative is determined by the inverse number, the sum of the products of different rows and columns..., generally not commonly used, use the row (column) expansion formula
Expand formula by row (column)
Yuzi style
algebraic cofactor
theorem
The determinant of order n is equal to the sum of the products of any of its row (column) elements and their corresponding algebraic cofactors
The sum of the products of any row (column) element of the determinant and the algebraic cofactor of another row (column) element is 0