search for: hermitian

Hi: I create a hermitian matrix and then perform its singular value decomposition. But when I put it back, I don't get the original hermitian matrix. I am having the same problem with spectral value decomposition as well. I am using R 1.7.0 on Windows. Here is my code: X <- matrix(rnorm(16)+1i*rnorm(16),4) X...

Hello everybody When one is working with complex matrices, "transpose" very nearly always means *Hermitian* transpose, that is, A[i,j] <- Conj(A[j,i]). One often writes A^* for the Hermitian transpose. I have only once seen a "real-life" case where transposition does not occur simultaneously with complex conjugation. And I'm not 100% sure that that wasn't a mistake. Matlab and Oc...

...n(Re(eigen(A,F,T)$values)) [1] 2.521153e-10 > and the eigenvectors appear to behave themselves too. Also, can I raise a doco? The documentation for eigen() is not entirely transparent with regard to the 'symmetric' argument. For complex matrices, 'symmetric' should read 'Hermitian': > B <- matrix(c(2,1i,-1i,2),2,2) # 'B' is Hermitian > eigen(B,F,T)$values [1] 3+0i 1+0i > eigen(B,T,T)$values # answers agree as expected if 'symmetric' means 'Hermitian' [1] 3 1 > C <- matrix(c(2,1i,1i,2),2,2) # 'C' is symmetric...

I'm trying to test if a correlation matrix is positive semidefinite. My understanding is that a matrix is positive semidefinite if it is Hermitian and all its eigenvalues are positive. The values in my correlation matrix are real and the layout means that it is symmetric. This seems to satisfy the Hermitian criterion so I figure that my real challenge is to check if the eigenvalues are all positive. I've tried to use eigen(base) to dete...

...; > One property of "Squash and merge" is that it will add intermediate > commits as bullet points (`* `). In many cases the merger does not spend > more time cleaning up the description so a commit may look like: > > ``` > RFC: treat small negative λ as 0 for sqrt(::Hermitian) (#35057) > > * treat small negative λ as 0 for sqrt(::Hermitian) and log(::Hermitian) > > * typo > > * added tests, docs; removed rtol argument for log > > * don't ask for rtol so close to eps(Float64) > ``` There are some inelegant ways to workaroun...

...hat R has some holes in the solution of some of the linear algebra problems that may arise. It looks like Jim Ramsay used a quick and dirty approach to the generalized eigenproblem by using B^(-1) %*% A, which is usually not too successful due to issues with condition of B and making a symmetric/Hermitian problem unsymmetric. In short, the problem is stated as follows: Find the eigenvalues e and vectors v that satisfy A v = e B v There is a matrix form (I think A V = B V E is usual, though I tend to work on them one at a time in my mind.) The real trouble is that A and B can have...

On Fri, Sep 11, 2020 at 6:53 PM David Blaikie <dblaikie at gmail.com> wrote: > Is there any observable difference between "Squash and Merge" or "Rebase > and Merge" when "enforce linear history" is enabled, then? > "Squash and Merge" will only generate one commit. > > On Fri, Sep 11, 2020 at 3:45 PM Stephen Neuendorffer via llvm-dev

Hello all, I was wondering if there is a function in R that only computes the eigenvector corresponding to the largest/smallest eigenvalue of an arbitrary real matrix. Thanks Minh -- Living on Earth may be expensive, but it includes an annual free trip around the Sun.

Dear R-helpers, could anybody explain me briefly what is the difference between eigenvectors returned by 'eigen' and 'svd' functions and how they are related? Thanks in advance Ondrej Mikula

from ?eigen symmetric: if 'TRUE', the matrix is assumed to be symmetric (or Hermitian if complex) and only its lower triangle is used. If 'symmetric' is not specified, the matrix is inspected for symmetry. I think that could mislead a naive reader as it suggests that, with symmetric=TRUE, the result of eigen() (vectors and values) depends only on the lo...

...9s for PIII Xeon), I realized that R may treat the matrix as a general matrix rather than symmetric except the abnormal case. To confirm this, I modified the R_LapackPP.cc in Matrix package and it turned out that is.MMatrix() failed to return true. Hence if (checkClass(classes, "Hermitian")) return new LaSymmMatDouble(x); is not executed in static LaMatDouble* asLaMatrix(SEXP x). Instead if (isMatrix(x)) { return new LaGenMatDouble(x); } is used. After replaced return new LaGenMatDouble(x); with return new LaSymmMatDouble(x);...

Hi, It is my understanding that the eigenvectors of a circulant matrix are given as follows: 1,omega,omega^2,....,omega^{p-1} where the matrix has dimension given by p x p and omega is one of p complex roots of unity. (See Bellman for an excellent discussion on this). The matrix created by the attached row and obtained using the following commands indicates no imaginary parts for the