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Eigenvalue problem on non-Hermitian matrix
You can think of it like this: If there is an invertible V such that inv(V)*H*V=D, then you can expect that the matrix myW = inv...

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Seasonal Breakdown from a Time Series data
Perhaps the trenddecomp function would be useful? It has an optional input period where a vector of several periods can also be ...

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How to find all the downstream nodes from a node in a graph?
Looking at this again due to the recent comment added, it might be simpler to use a directed graph instead of an undirected one:...

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Which solver should I use to solve a square and symmetric, linear system of equations?
The first thing to check is the size and density of your matrix. The SYMMLQ function you mentioned is one of a group of methods ...

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Can we compute the graph Laplacian matrix for a directed graph?
It depends how you want to define it, there is no one consistent definition of what the graph laplacian of a directed graph is. ...

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eigs using 'smallestabs' vs scalar
Hi Jack, I had initially misunderstood that you were getting different results when passing in 'smallestabs' vs. passing in the...

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missing eigenvector when using eig on defective matrix
The short answer is that this is a case where a small change in the input matrix has a large effect on the eigenvectors being co...

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THE GRAPH FUNCTION DOESN'T CONSIDER WEIGHTS
Hard to say what's going wrong without seeing your code. Here's an example where you can see the weights being used to decide on...

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mldivide (backslash): advantage by using sparse matrix instead of a full matrix with respect to the quality of the results?
The condition estimate used in mldivide to decide if a warning should be given is much less accurate for the sparse case. This i...

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LDL does not support complex symmetric matrices
Largely the reason LDL doesn't support this is that it's less commonly requested for complex symmetric matrices than for complex...

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Inconsistency in behavior of SVD
Firstly, I agree completely with John's great explanations above: Any singular value below eps*first singular value should be tr...

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Accuracy Problem when solving linear equation system using: lu(S) vs. decomposition(S,'lu')
The version in decomposition does some optional steps of iterative refinement: It uses the same solution you have above based on...

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Need help fixing errors on code written in old MATLAB syntax
I'd also recommend replacing the calls svd(A) and svd(A, 0) with calling svd(A, 'econ'), since the code here is only using the f...

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Different results on different computers, Matlab 2021b - 64 bit, windows 64 bit, both Intel chips
First, about "which value to trust?" Both values are equally trustworthy, the differences in results come down to applying the ...

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eigs with Extended Capabilities
The first of these would only be useful if you need to apply EIGS to many problems in parallel, in which case each of these coul...

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How to parallelize many small SVD's on a GPU
As of R2021b, there is a function pagesvd which is supported on both CPU and distributed arrays. It's not supported for gpuArray...

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How does shortestpath function work?
Every edge has a number, which is the order in which they appear in the Edges table (try displaying g.Edges). The edgepath conta...

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Eigs passes the wrong StartVector
The standard method used in EIGS is only efficient for matrices that are quite large. When eigs detects that the input matrix is...

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How to enhance the performance of Matalb's function sqrtm?
Not in general. You might be able to find a cheaper but less accurate way to compute this, but if that's acceptable would depend...

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fastest path between more than two nodes
To compute simply the shortest-path distance, you can use the distances function and pass in a graph object you've constructed u...

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Follow a complex eigenvalue in a spectrum at different times
You could try using the matchpairs function: rng default; d = randn(20, 1) + 1i*randn(20, 1); d2 = d + 0.1*(randn(20, 1) + 1i...

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Error using eig in Matlab 2021b by using Parallels 17 of Macbook Pro (M1 )
Since MATLAB is trying to load a .dll file, I'm assuming you're running a Windows VM on this Macbook Pro. MATLAB doesn't support...

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use of svds with function handles
The svds function needs to be able to apply both A*x and A'*x, so your function handle should accept a second input which is eit...

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How to compute cholesky to all slice of a tensor?
There isn't another way to do this right now. We have functions that do other linear algebra operations to each page of an ND-ar...

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Why does mldivide solve equations so fast that FORTRAN can't compare it？
MATLAB's mldivide uses multithreading. It doesn't use the GPU unless you have the Parallel Computing Toolbox and are using the g...

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How to highlight single edges in an undirected graph?
Do you still want the multiple edges to be displayed? If not, you can use the simplify command to reduce all multiple edges to j...

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Unable to find out left eigen vectors of symbolic matrix
The left eigenvectors are still expressed as right eigenvectors of M', meaning they satisfy a slightly different equation: syms...

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Program to find connected and non-isomorphic graphs
In the last loop, you are checking if adj is isomorphic to any previous graph. If there is one graph that adj is not isomorphic ...

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How can I invert a big matrix e.g. 1000-by-1000
When running inv on this matrix, there's a warning: >> M = inv(current_Fit_Mat); Warning: Matrix is close to singular or badly...

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Add an automatic TOC to an .mlx
You can go the "Insert" tab (just to the right of where it says "Live Editor" on top of the MATLAB window) and there's a button ...

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