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The stabilizer subgroup of the standard flag is the group of invertible upper triangular matrices.. More generally, the stabilizer of a flag (the linear operators on V such that () < for all i) is, in matrix terms, the algebra of block upper triangular matrices (with respect to an adapted basis), where the block sizes .
A solution of a linear system is an assignment of values to the variables ,, …, such that each of the equations is satisfied. The set of all possible solutions is called the solution set. [5] A linear system may behave in any one of three possible ways: The system has infinitely many solutions.
Flag varieties can be defined in various degrees of generality. A prototype is the variety of complete flags in a vector space V over a field F, which is a flag variety for the special linear group over F. Other flag varieties arise by considering partial flags, or by restriction from the special linear group to subgroups such as the symplectic ...
Gordon, Bender and Herman first showed its use in image reconstruction; [1] whereas the method is known as Kaczmarz method in numerical linear algebra. [ 2 ] [ 3 ] An advantage of ART over other reconstruction methods (such as filtered backprojection ) is that it is relatively easy to incorporate prior knowledge into the reconstruction process.
The Kaczmarz method or Kaczmarz's algorithm is an iterative algorithm for solving linear equation systems =.It was first discovered by the Polish mathematician Stefan Kaczmarz, [1] and was rediscovered in the field of image reconstruction from projections by Richard Gordon, Robert Bender, and Gabor Herman in 1970, where it is called the Algebraic Reconstruction Technique (ART). [2]
The characteristic linear system of a family of curves on an algebraic surface Y for a curve C in the family is a linear system formed by the curves in the family that are infinitely near C. [ 4 ] In modern terms, it is a subsystem of the linear system associated to the normal bundle to C ↪ Y {\displaystyle C\hookrightarrow Y} .
Most flags are traditionally created at a height-to-width ratio of 4x6 or 3x5, but football field flags are constructed in a 1x2 ratio — necessary to keep the lowest few stripes from reaching 10 ...
For example, in geometry, two linearly independent vectors span a plane. To express that a vector space V is a linear span of a subset S, one commonly uses one of the following phrases: S spans V; S is a spanning set of V; V is spanned or generated by S; S is a generator set or a generating set of V.