Copositive matrix
Encyclopedia
In mathematics, specifically linear algebra
, a real
matrix
A is copositive if
for every nonnegative vector
. 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.
Linear algebra
Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...
, a real
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
matrix
Matrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
A is copositive if
for every nonnegative vector
. The collection of all copositive matrices is a proper cone; it includes as a subset the collection of real positive-definite matricesPositive-definite matrix
In linear algebra, a positive-definite matrix is a matrix that in many ways is analogous to a positive real number. The notion is closely related to a positive-definite symmetric bilinear form ....
.
Copositive matrices find applications in economics, operations research
Operations research
Operations research is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations...
, and statistics.