2.2.2. LU decomposition method
Other non-direct approaches to find the determinant of matrices are the LU and QR methods. The complete
explanation of these methods is not within the scope of this paper. The following steps are undertaken to
perform the decomposition on a square matrix, i.e., matrix A is decomposed as
A ¼ L U; ð2:2Þ
where L is a lower triangular matrix and U is an upper triangular matrix. On decomposition, both L and U
replace the matrix A. The new changed row index is returned for performing the back substitution later.
It performs forward and backward substitutions on an LU decomposed matrix to find out the solution vector
for a linear set of equations. Here, V is the right-hand side input vector and R is the row index. Some methods
can be used to improve imperfect solutions found by the LU decomposition method. This method must be
applied to the original matrix. It should then be solved a set of linear equations using the LU decomposition
method. The singular value decomposition on a matrix, i.e., any M · N matrix A, where M >= N, is decomposed
as
2.2.2. LU decomposition methodOther non-direct approaches to find the determinant of matrices are the LU and QR methods. The completeexplanation of these methods is not within the scope of this paper. The following steps are undertaken toperform the decomposition on a square matrix, i.e., matrix A is decomposed asA ¼ L U; ð2:2Þwhere L is a lower triangular matrix and U is an upper triangular matrix. On decomposition, both L and Ureplace the matrix A. The new changed row index is returned for performing the back substitution later.It performs forward and backward substitutions on an LU decomposed matrix to find out the solution vectorfor a linear set of equations. Here, V is the right-hand side input vector and R is the row index. Some methodscan be used to improve imperfect solutions found by the LU decomposition method. This method must beapplied to the original matrix. It should then be solved a set of linear equations using the LU decompositionmethod. The singular value decomposition on a matrix, i.e., any M · N matrix A, where M >= N, is decomposedas
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