Implementation of LU-decomposition and QR-decomposition of the matrix A with the choice of the leading element by column Also implemented the decomposition check and comparison of the matrices LU and PA, where P is the row permutation matrix in the case of LU-decomposition and matrices QR and A in the case of QR-decomposition.
Also, using the LU and QR decompositions, were found:
- The determinant of the matrix A;
- System of linear equations solution Ax = b;
- Matrix A^(-1);
- Condition number of matrix A.