triangular matrices 예문

• Their Lie algebras consist of upper and lower strictly triangular matrices.
• The upper triangular matrices are precisely those that stabilize the standard flag.
• (The Stirling numbers of the first and triangular matrices.
• The M鯾ius transformations fixing  " are just the upper triangular matrices.
• The final algorithm looks very much like an iterated product of triangular matrices.
• The group \ Gamma would be the upper triangular matrices with integral coefficients.
• Let be the Borel subgroup of upper triangular matrices and the subgroup of diagonal matrices.
• However, operations mixing upper and lower triangular matrices do not in general produce triangular matrices.
• However, operations mixing upper and lower triangular matrices do not in general produce triangular matrices.
• Because matrix equations with triangular matrices are easier to solve, they are very important in numerical analysis.
• In the GL ( 3, 2 ) representation, a Sylow 2-subgroup consists of the upper triangular matrices.
• By way of an example, let us apply this definition to recover the finite-dimensional upper-triangular matrices.
• Together these facts mean that the upper triangular matrices form a subalgebra of the associative algebra of square matrices for a given size.
• The Lie algebra of all upper triangular matrices is often referred to as a Borel subalgebra of the Lie algebra of all square matrices.
• The stabilizer subgroup of a complete flag is the set of invertible upper triangular matrices with respect to any basis adapted to the flag.
• As we mentioned, a necessary condition for a group to contain a lattice is that it be upper triangular matrices or the affine groups.
• Because I do not expect anything more than upper triangular matrices, the procedure is expected to be short and simple ( no vector subspaces are required ).
• Applying this argument repeatedly to shows that there is an orthonormal basis of consisting of eigenvectors of with acting as upper triangular matrices with zeros on the diagonal.
• All these results hold if " upper triangular " is replaced by " lower triangular " throughout; in particular the lower triangular matrices also form a Lie algebra.
• The group of invertible lower triangular matrices is such a subgroup, since it is the stabilizer of the standard flag associated to the standard basis in reverse order.