how to calculate the lu decomposition of a matrix in matlab

To calculate the LU decomposition of a matrix in MATLAB, you can use the lu function. This function returns the lower triangular matrix L, upper triangular matrix U, and the permutation matrix P such that A = P*L*U, where A is the input matrix.

Here's an example:

main.m
A = [1 2 3; 4 5 6; 7 8 9];
[L,U,P] = lu(A);
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In this example, A is the input matrix, and L, U and P are the outputs of the lu function. You can then use these matrices as needed, for example to solve a system of linear equations.

main.m
b = [1; 2; 3];
x = U \ (L \ (P*b));
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In this example, b is the right-hand side vector of the system of linear equations, and x is the solution vector. The backslash operator (\) is used to solve the system.

Note that the permutation matrix P is used to avoid division by zero in the factorization process when pivoting is needed.