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Fredholm's Theorem


Fredholm's theorem states that, if A is an m×n matrix, then the orthogonal complement of the row space of A is the null space of A, and the orthogonal complement of the column space of A is the null space of A^_|_,

(RowA)^_|_=NullA
(1)
(ColA)^_|_=NullA^_|_.
(2)

See also

Column Space, Null Space, Orthogonal Decomposition, Row Space

This entry contributed by Viktor Bengtsson

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Cite this as:

Bengtsson, Viktor. "Fredholm's Theorem." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/FredholmsTheorem.html

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