- {\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...
- 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...
- respectively, the
product order (also
called the
coordinatewise order or
componentwise order) is a
partial order ≤ {\displaystyle \leq } on the
Cartesian product...
-
underlying sets of
several rings (possibly an infinity),
equipped with
componentwise operations. It is a
direct product in the
category of rings.
Since direct...
- {\displaystyle {\boldsymbol {\beta }}\geq {\boldsymbol {0}}}
defined componentwise—that is, each
component must be
either positive or zero. Box-constrained...
- 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...
-
field via
sequences of reals. In fact we can add and
multiply sequences componentwise; for example: ( a 0 , a 1 , a 2 , … ) + ( b 0 , b 1 , b 2 , … ) = (...
- {\displaystyle F^{n}} of the n-tuples of
elements of F is a
vector space for
componentwise addition and
scalar multiplication,
whose dimension is n. The one-to-one...
- with
multiplication defined in a
specific way (different from the
componentwise multiplication) and an
involution known as conjugation. The product...
