Finding a low-rank basis in a matrix subspace
... certificates. An alternative, less cheap, but exact method uses simultaneous diagonalization, which are applicable when d ≤ min(m, n). Applying these methods will often be successful when a rank-one basis exists, but fails if not. This tensor approach seems to have been overseen in the discrete opti ...
... certificates. An alternative, less cheap, but exact method uses simultaneous diagonalization, which are applicable when d ≤ min(m, n). Applying these methods will often be successful when a rank-one basis exists, but fails if not. This tensor approach seems to have been overseen in the discrete opti ...
Simple exponential estimate for the number of real zeros of
... The operator L G 2) is called irreducible, if the monodromy group of this operator is irreducible, i.e. the operators M^ have no common invariant nontrivial subspace. For Fuchsian operators (equations) an equivalent algebraic formulation can be given as follows: L is irreducible if and only if it ad ...
... The operator L G 2) is called irreducible, if the monodromy group of this operator is irreducible, i.e. the operators M^ have no common invariant nontrivial subspace. For Fuchsian operators (equations) an equivalent algebraic formulation can be given as follows: L is irreducible if and only if it ad ...
Vector Spaces
... Definition 15. The span of the vectors v 1 , v 2 , . . . , v n is the set of all linear combinations of v 1 , v 2 , . . . , v n : it is written span{v1 , v 2 , . . . , v n }. In a vector space, all finite sums of the form λ1 v 1 + λ2 v 2 + · · · + λn v n are well-defined, i.e., have an unambiguous me ...
... Definition 15. The span of the vectors v 1 , v 2 , . . . , v n is the set of all linear combinations of v 1 , v 2 , . . . , v n : it is written span{v1 , v 2 , . . . , v n }. In a vector space, all finite sums of the form λ1 v 1 + λ2 v 2 + · · · + λn v n are well-defined, i.e., have an unambiguous me ...
on the complexity of computing determinants
... running time of the used algorithms. A classical methodology is to compute the results via Chinese remaindering. Then the standard analysis yields a number of fixed radix, i.e. bit operations for a given problem that is essentially (within polylogarithmic factors) bounded by the number of field oper ...
... running time of the used algorithms. A classical methodology is to compute the results via Chinese remaindering. Then the standard analysis yields a number of fixed radix, i.e. bit operations for a given problem that is essentially (within polylogarithmic factors) bounded by the number of field oper ...
Course Notes - Mathematics for Computer Graphics トップページ
... constrast, dual quaternion and axis-angle presentation are useful in rigid transformation (rotation and translation altogether). These mathematical concepts have become quite popular and have a success to some extent in our graphics community. In this section we therefore take a brief look at the or ...
... constrast, dual quaternion and axis-angle presentation are useful in rigid transformation (rotation and translation altogether). These mathematical concepts have become quite popular and have a success to some extent in our graphics community. In this section we therefore take a brief look at the or ...