02:00 - 21:0021:00 - 00:00
In mathematics, a symmetric matrix
M
{\displaystyle M}
with real entries is positive-definite if the real number
z
T
M
z
{\displaystyle z^{\operatorname {T} }Mz}
is positive for every nonzero real column vector
z
,
{\displaystyle z,}
where
z
T
{\displaystyle z^{\operatorname {T} }}
is the transpose...
0
Let $s\mapsto A_s$ be an increasing right continuous function, $s\geq 0$. Then define $A_s^{-1}:=\inf\{t\geq 0: A_t>s\}$ with the convention $\inf\{\emptyset\}=\infty$. By definition the map $s\mapsto A_s^{-1}$ in increasing so one can define $A_{s-}^{-1}:=\lim_{h\rightarrow 0} A_{s-h}^{-1}$ the...
In mathematics, a full subcategory A of a category B is said to be reflective in B when the inclusion functor from A to B has a left adjoint.: 91 This adjoint is sometimes called a reflector, or localization. Dually, A is said to be coreflective in B when the inclusion functor has a right adjoint.
Informally, a reflector acts as a kind of completion operation. It adds in any "missing" pieces of the structure in such a way that reflecting it again has no further effect.
== Definition ==
A full subcategory A of a category B is said to be reflective in B if for each B-object B there exists ...
0
02:00 - 21:0021:00 - 00:00
