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The Fredholm alternative is the statement that, for every non-zero fixed complex number, either the first equation has a non-trivial solution, or the second equation has a solution for all (). A sufficient condition for this statement to be true is for K ( x , y ) {\displaystyle K(x,y)} to be square integrable on the rectangle [ a , b ] × [ a ...
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[1] [2] A transformation A ↦ P −1 AP is called a similarity transformation or conjugation of the matrix A . In the general linear group , similarity is therefore the same as conjugacy , and similar matrices are also called conjugate ; however, in a given subgroup H of the general linear group, the notion of conjugacy may be more restrictive ...
In numerical analysis and linear algebra, lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix decomposition). The product sometimes includes a permutation matrix as well. LU decomposition can be viewed as the matrix form of Gaussian elimination.
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In three-dimensional Euclidean space, these three planes represent solutions to linear equations, and their intersection represents the set of common solutions: in this case, a unique point. The blue line is the common solution to two of these equations. Linear algebra is the branch of mathematics concerning linear equations such as:
Intel said on Wednesday its deal for $7.86 billion in U.S. government subsidies restricts the company's ability to sell stakes in its chipmaking unit if it becomes an independent entity. The U.S ...
The rank–nullity theorem is a theorem in linear algebra, which asserts: the number of columns of a matrix M is the sum of the rank of M and the nullity of M ; and the dimension of the domain of a linear transformation f is the sum of the rank of f (the dimension of the image of f ) and the nullity of f (the dimension of the kernel of f ).
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