In other words, ? is triangularizable if there exists a basis such that every element of ? has an upper-triangular matrix representation in that basis.
22.
An incomplete Cholesky factorization is given by a sparse lower triangular matrix " K " that is in some sense close to " L ".
23.
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.
24.
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.
25.
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.
26.
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.
27.
This new matrix is the upper triangular matrix needed to perform an iteration of the QR decomposition . is now formed using the transpose of the rotation matrices in the following manner:
28.
Because the eigenvalues of a triangular matrix are its diagonal elements, for general matrices there is no finite method like gaussian elimination to convert a matrix to triangular form while preserving eigenvalues.
29.
Given a complex square matrix A, find a matrix P such that P-1 AP is an upper triangular matrix ( nothing more, need not be a Jordan form ).
30.
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.
