triangular matrix वाक्य
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- In other words, ? is triangularizable if there exists a basis such that every element of ? has an upper-triangular matrix representation in that basis.
- An incomplete Cholesky factorization is given by a sparse lower triangular matrix " K " that is in some sense close to " L ".
- 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.
- 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.
- 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.
- 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.
- 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:
- 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.
- 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 ).
- 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.
- 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.
- If the entries on the main diagonal of a ( upper or lower ) triangular matrix are all 1, the matrix is called ( upper or lower ) "'unitriangular " '.
- A more precise statement is given by the Jordan normal form theorem, which states that in this situation, " A " is similar to an upper triangular matrix of a very particular form.
- A central series is analogous in Lie theory to a adjoint action ( more prosaically, a basis in which each element is represented by a strictly upper triangular matrix ); compare Engel's theorem.
- Since the determinant of a triangular matrix is the product of its diagonal entries, if " T " is triangular, then Thus the eigenvalues of " T " are its diagonal entries.
- 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 ).
- 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 ).
- 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.
- In fact, a matrix " A " over a field containing all of the eigenvalues of " A " ( for example, any matrix over an algebraically closed field ) is similar to a triangular matrix.
- Property 5 says that the determinant on matrices is field, properties 11 and 12 can be used to transform any matrix into a triangular matrix, whose determinant is given by property 6; this is essentially the method of Gaussian elimination.
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