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Calculating the complexity of determinant of matrix with n columns?
Wiki User
∙ 12y ago
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).
Wiki User
∙ 12y ago
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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.
A rectangular arrangement of numbers in rows and columns?
It is a matrix or a determinant.
What is the minor of determinant?
The minor is the determinant of the matrix constructed by removing the row and column of a particular element. Thus, the minor of a34 is the determinant of the matrix which has all the same rows and columns, except for the 3rd row and 4th column.
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
What is the Time complexity of transpose of a matrix?
Transposing a matrix is O(n*m) where m and n are the number of rows and columns. For an n-row square matrix, this would be quadratic time-complexity.
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.
Why only square matrix have determinant?
The square matrix have determinant because they have equal numbers of rows and columns. <<>> Determinants are not defined for non-square matrices because there are no applications of non-square matrices that require determinants to be used.
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 rank of the determinant of 123456 its a 2 x 3 matrix?
A determinant is defined only for square matrices, so a 2x3 matrix does not have a determinant.Determinants are defined only for square matrices, so a 2x3 matrix does not have a determinant.
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.
Why is matrix named matrix?
Matrix derives from Latin "Mater" which means "mother". It was called this because the determinant, which is very central to matrix mathematics, changes when we remove columns or rows, so with simple words it's because a little matrix can be a part of a larger 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.
How to find x in a 2×2 matrix with a given determinant.?
For a matrix A, A is read as determinant of A and not, as modulus of A. ... sum of two or more elements, then the given determinant can be expressed as the sum
