“Fredholm alternative”的概念、定义、翻译、参考文献-科学参考

Fredholm alternative

Mathematics

A simple form of the Fredholm alternative states that for a square matrix A

$\begin{array}{rcl} either v & = & A v + b has a solution v for all b \\ or v & = & A v has a non-zero solution . \end{array}$

The former holds when A–I is invertible and the latter when it is singular. The more general Fredholm alternative is an important result in functional analysis, where ℝⁿ is replaced by an infinite-dimensional Hilbert space and A is replaced by a self-adjoint compact operator.

单词	Fredholm alternative
释义	Fredholm alternative Mathematics A simple form of the Fredholm alternative states that for a square matrix A $\begin{array}{rcl} either v & = & A v + b has a solution v for all b \\ or v & = & A v has a non-zero solution . \end{array}$ The former holds when A–I is invertible and the latter when it is singular. The more general Fredholm alternative is an important result in functional analysis, where ℝⁿ is replaced by an infinite-dimensional Hilbert space and A is replaced by a self-adjoint compact operator.
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