answersLogoWhite

0

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).

User Avatar

Wiki User

12y ago

Still curious? Ask our experts.

Chat with our AI personalities

CoachCoach
Success isn't just about winning—it's about vision, patience, and playing the long game.
Chat with Coach
RafaRafa
There's no fun in playing it safe. Why not try something a little unhinged?
Chat with Rafa
TaigaTaiga
Every great hero faces trials, and you—yes, YOU—are no exception!
Chat with Taiga

Add your answer:

Earn +20 pts
Q: Calculating the complexity of determinant of matrix with n columns?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Continue Learning about Math & Arithmetic

What is the difference between matrices and determinants?

Both matrix and determinants are the part of business mathematics. Both are useful for solving business problem. Both are helpful for calculation of each other. For calculation of inverse of matrix, we need to calculate the determinant. For calculating the value of 3X3 matrix or more matrix, we need to divide determinants in sub-matrix. but there are many differences between matrix and determinants which we can explain in following points. 1. Matrix is the set of numbers which are covered by two brackets. Determinants is also set of numbers but it is covered by two bars. 2. It is not necessary that number of rows will be equal to the number of columns in matrix. But it is necessary that number of rows will be equal to the number of columns in determinant. 3. Matrix can be used for adding, subtracting and multiplying the coefficients. Determinant can be used for calculating the value of x, y and z with Cramer's Rule. By Er. Hafijullah


When is a square matrix said to be diagonisable?

When its determinant is non-zero. or When it is a linear transform of the identity matrix. or When its rows are independent. or When its columns are independent. These are equivalent statements.


What is diff between matrices and determinants?

actually MATRICES is the plural of matrix which means the array of numbers in groups and columns in a rectangular table... and determinant is used to calculate the magnitude of a matrix....


What is the determinant of a 2x3 matrix?

The determinant function is only defined for an nxn (i.e. square) matrix. So by definition of the determinant it would not exist for a 2x3 matrix.


What does determine mean in maths?

In Algebra, the word determinant is a special number which is associated to any square matrix. Like for example, a rectangular array of numbers where the finite number of rows and columns are equal. Therefore, the meaning of a determinant is a scale factor for measuring wherever the matrix is regarded.