In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero. A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors (in addition to the zero vector).
A norm must also satisfy certain properties pertaining to scalability and additivity which are given in the formal definition below.
A simple example is the 2-dimensional Euclidean space R2 equipped with the Euclidean norm. Elements in this...
In mathematics, specifically linear algebra, a real matrix A is copositive if
x
T
A
x
≥
0
{\displaystyle x^{T}Ax\geq 0}
for every nonnegative vector
x
≥
0
{\displaystyle x\geq 0}
. The collection of all copositive matrices is a proper cone; it includes as a subset the collection of real positive-definite matrices.
Copositive matrices find applications in economics, operations research, and statistics.
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