When calculating the determinant, we often use the properties of the determinant and convert it into a triangular determinant for calculation. For example, the general steps to transform into an upper triangular determinant are:

　　If the first element in the first column is , first exchange the first row with other rows so that the first element in the first column is not ; then, multiply the first row by the appropriate number and add it to the other rows , so that Except for the first element, all other elements in the first column are ;

　　Then use the same method to process the remaining lower first-order determinant after removing the first row and the first column, and continue in this way until it becomes an upper triangular determinant. At this time, the product of the elements on the main diagonal is the determinant value.

　　Note: Most of today's computer programs for computing general determinants are designed according to the above method. It can be proved that using the above method to calculate order determinant requires approximately number of arithmetic operations. Any modern microcomputer can calculate the value of a determinant of order in a fraction of a second , using approximately operations . If we use the definition of determinant to calculate, the amount of calculation is about times, which is obviously a very huge value.