- {\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...
- x↑y{\displaystyle x\uparrow y}
denotes the
componentwise maximum and x↓y{\displaystyle x\downarrow y} the
componentwise minimum of x{\displaystyle x} and y{\displaystyle...
-
finding a
Tarski fixed-point. They
consider two
kinds of lattices:
componentwise ordering and
lexicographic ordering. They
consider two
kinds of input...
- {\displaystyle {\boldsymbol {\beta }}\geq {\boldsymbol {0}}}
defined componentwise—that is, each
component must be
either positive or zero. Box-constrained...
- However, the
existence of a
componentwise derivative does not
guarantee the
existence of a derivative, as
componentwise convergence in a
Hilbert space...
- 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 , ⋯...
- 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 ordering ≤ {\displaystyle \leq } on the Cartesian...
-
Complex coordinate space is a
vector space over the
complex numbers, with
componentwise addition and
scalar multiplication. The real and
imaginary parts of...
- 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...
