- {\displaystyle v_{i}} , then
componentwise addition is ( u + v ) i = u i + v i {\displaystyle (u+v)_{i}=u_{i}+v_{i}} .
Componentwise operations can be defined...
-
finding a
Tarski fixed-point. They
consider two
kinds of lattices:
componentwise ordering and
lexicographic ordering. They
consider two
kinds of input...
- respectively, the
product order (also
called the
coordinatewise order or
componentwise order) is a
partial ordering ≤ {\displaystyle \leq } on the Cartesian...
- In mathematics,
majorization is a
preorder on
vectors of real numbers. For two such vectors, x , y ∈ R n {\displaystyle \mathbf {x} ,\ \mathbf {y} \in...
- {\displaystyle {\boldsymbol {\beta }}\geq {\boldsymbol {0}}}
defined componentwise—that is, each
component must be
either positive or zero. Box-constrained...
- then ∏ i ∈ I R i {\textstyle \prod _{i\in I}R_{i}} is a ring with
componentwise addition and multiplication. Let R be a
commutative ring and a 1 , ⋯...
- above,
using the
Cartesian product with the
operation of
addition being componentwise, and the
scalar multiplication just
distributing over all the components...
- However, the
existence of a
componentwise derivative does not
guarantee the
existence of a derivative, as
componentwise convergence in a
Hilbert space...
- a
vector space over K (Halmos 1974, §18) by
defining the
operations componentwise: (v1, w1) + (v2, w2) = (v1 + v2, w1 + w2) α (v, w) = (α v, α w) for...
- of
elements of K {\displaystyle \mathbb {K} } is a
vector space for
componentwise addition ( x n ) n ∈ N + ( y n ) n ∈ N = ( x n + y n ) n ∈ N , {\displaystyle...
