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).
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
To solve for the log determinant of a matrix, you typically compute the determinant first and then take the logarithm of that value. For a positive definite matrix ( A ), the log determinant can be expressed as ( \log(\det(A)) ). If ( A ) is decomposed using methods like Cholesky decomposition, you can simplify the computation by calculating the determinant of the triangular matrix and then applying the logarithm. Additionally, in some contexts, such as with Gaussian distributions, the log determinant can be efficiently computed using properties of matrix trace and eigenvalues.
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.
If the determinant of a matrix is 0, it indicates that the matrix is singular, meaning it does not have an inverse. This also implies that the rows or columns of the matrix are linearly dependent, meaning at least one row or column can be expressed as a linear combination of the others. In the context of systems of equations, a zero determinant suggests that the system may have either no solutions or infinitely many solutions.
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....
It is a matrix or a 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.
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
To solve for the log determinant of a matrix, you typically compute the determinant first and then take the logarithm of that value. For a positive definite matrix ( A ), the log determinant can be expressed as ( \log(\det(A)) ). If ( A ) is decomposed using methods like Cholesky decomposition, you can simplify the computation by calculating the determinant of the triangular matrix and then applying the logarithm. Additionally, in some contexts, such as with Gaussian distributions, the log determinant can be efficiently computed using properties of matrix trace and eigenvalues.
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.
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.
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.
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....
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.
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.
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.
To find the determinant of a matrix on a Casio fx-991MS calculator, you first need to enter the matrix into the calculator using the matrix mode. Then, navigate to the matrix menu and select the matrix you want to find the determinant of. Finally, choose the option to calculate the determinant, and the calculator will display the result. Remember that the determinant of a matrix is a scalar value that represents certain properties of the matrix.