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https://math.answers.com/math-and-arithmetic/Calculating_the_complexity_of_determinant_of_matrix_with_n_columns

Calculating the complexity of determinant of matrix with n columns? - Answers

Using the method derived from the usual definition using the minors, the complexity is O(n!). But it seems that one could just do the Gaussian elimination on the matrix, turning the matrix into a triangular one while keeping track of any neccessary row swaps, and then just multiply the values of the diagona. This method would get the complexity of O(n*n).



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Calculating the complexity of determinant of matrix with n columns? - Answers

https://math.answers.com/math-and-arithmetic/Calculating_the_complexity_of_determinant_of_matrix_with_n_columns

Using the method derived from the usual definition using the minors, the complexity is O(n!). But it seems that one could just do the Gaussian elimination on the matrix, turning the matrix into a triangular one while keeping track of any neccessary row swaps, and then just multiply the values of the diagona. This method would get the complexity of O(n*n).



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https://math.answers.com/math-and-arithmetic/Calculating_the_complexity_of_determinant_of_matrix_with_n_columns

Calculating the complexity of determinant of matrix with n columns? - Answers

Using the method derived from the usual definition using the minors, the complexity is O(n!). But it seems that one could just do the Gaussian elimination on the matrix, turning the matrix into a triangular one while keeping track of any neccessary row swaps, and then just multiply the values of the diagona. This method would get the complexity of O(n*n).

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      Using the method derived from the usual definition using the minors, the complexity is O(n!). But it seems that one could just do the Gaussian elimination on the matrix, turning the matrix into a triangular one while keeping track of any neccessary row swaps, and then just multiply the values of the diagona. This method would get the complexity of O(n*n).

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