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minor typo fix in README #106

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May 23, 2022
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minor typo fix in README #106

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2 changes: 1 addition & 1 deletion README.md
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Expand Up @@ -84,7 +84,7 @@ This currently supports the infinite-dimensional QL factorization for perturbati
A = BandedMatrix(-3 => Fill(7/10,∞), -2 => Fill(1,∞), 1 => Fill(2im,∞))
ql(A - 5*I)
```
The infinite-dimensional QL factorization is a subtly thing: its defined when the operator has non-positive Fredholm index, and if the Fredholm index is not zero, it may not be unique. For the Bull head matrix `A`, here are plots of `ql(A-λ*I).L[1,1]` alongside the image of the symbol `A`, which depicts the essential spectrum of `A` and where the Fredholm index changes. Note we have two plots as the regions with negative Fredholm index have multiple QL factorizations. Where the Fredholm index is positive, the QL factorization doesn't exist and is depected in black.
The infinite-dimensional QL factorization is a subtly thing: its defined when the operator has non-positive Fredholm index, and if the Fredholm index is not zero, it may not be unique. For the Bull head matrix `A`, here are plots of `ql(A-λ*I).L[1,1]` alongside the image of the symbol `A`, which depicts the essential spectrum of `A` and where the Fredholm index changes. Note we have two plots as the regions with negative Fredholm index have multiple QL factorizations. Where the Fredholm index is positive, the QL factorization doesn't exist and is depicted in black.

<img src=https://github.com/JuliaMatrices/InfiniteLinearAlgebra.jl/raw/master/images/ql1.png width=500 height=400>
<img src=https://github.com/JuliaMatrices/InfiniteLinearAlgebra.jl/raw/master/images/ql2.png width=500 height=400>
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