Hence, the lower triangular matrix " L " we are looking for is calculated as
2.
The factorization is stored as a lower triangular matrix, with the elements in the upper triangle set to zero.
3.
The Crout algorithm is slightly different and constructs a lower triangular matrix and a " unit upper triangular " matrix.
4.
The LU decomposition factorizes a matrix into a lower triangular matrix " L " and an upper triangular matrix " U ".
5.
An incomplete Cholesky factorization is given by a sparse lower triangular matrix " K " that is in some sense close to " L ".
6.
Doolittle's method returns a unit lower triangular matrix and an upper triangular matrix, while the Crout method returns a lower triangular matrix and a unit upper triangular matrix.
7.
Doolittle's method returns a unit lower triangular matrix and an upper triangular matrix, while the Crout method returns a lower triangular matrix and a unit upper triangular matrix.
8.
For instance, the sum of an upper and a lower triangular matrix can be any matrix; the product of a lower triangular with an upper triangular matrix is not necessarily triangular either.
9.
For example, we can conveniently require the lower triangular matrix " L " to be a unit triangular matrix ( i . e . set all the entries of its main diagonal to ones ).
10.
An example of a group of symplectic matrices is the group of three symplectic 2x2-matrices consisting in the identity matrix, the upper triagonal matrix and the lower triangular matrix, each with entries 0 and 1.
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