# \#linearalgebra

**URL:** https://discourse.julialang.org/tag/linearalgebra/126.md

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## [Running out of RAM with repeated cholesky solves](https://discourse.julialang.org/t/running-out-of-ram-with-repeated-cholesky-solves/136044)

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**Author:** [@falconflier](https://discourse.julialang.org/u/falconflier)\
**Replies:** 16\
**Last updated:** [September 3, 2026, 8:58am UTC](https://discourse.julialang.org/t/running-out-of-ram-with-repeated-cholesky-solves/136044 "2026-09-03T08:58:43Z")

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Hello, I have a system in which I need to repeatedly solve an electrostatics problem with an evolving charge configuration. When I left my program running overnight, I came back to find that RAM utilization had accumula…

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## [Looking for advice on package for lazily evaluated kernel matrix on the GPU](https://discourse.julialang.org/t/looking-for-advice-on-package-for-lazily-evaluated-kernel-matrix-on-the-gpu/139089)

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**Author:** [@trevorgloe](https://discourse.julialang.org/u/trevorgloe)\
**Replies:** 2\
**Last updated:** [September 1, 2026, 12:37am UTC](https://discourse.julialang.org/t/looking-for-advice-on-package-for-lazily-evaluated-kernel-matrix-on-the-gpu/139089 "2026-09-01T00:37:29Z")

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I am working on creating a package for lazily evaluated kernel matrices, which will work on the GPU via KernelAbstractions. The idea is to create a central object (LazyKernelMatrix) which does not allocate and evaluates …

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## [Compiler mis-recognizes contiguous reinterpreted matrices?](https://discourse.julialang.org/t/compiler-mis-recognizes-contiguous-reinterpreted-matrices/138979)

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**Author:** [@bremez](https://discourse.julialang.org/u/bremez)\
**Replies:** 11\
**Last updated:** [August 25, 2026, 2:02pm UTC](https://discourse.julialang.org/t/compiler-mis-recognizes-contiguous-reinterpreted-matrices/138979 "2026-08-25T14:02:33Z")

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I am implementing an ODE to use with OrdinaryDiffEq. I am simultaneously evolving in time multiple quantities, which are combinations of vectors and matrices, some real and some complex. The approach I took has been to g…

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## [\[ANN\] AcceleratedRPCholesky.jl: A fast way to find near-optimal low-rank approximations of kernel matrices](https://discourse.julialang.org/t/ann-acceleratedrpcholesky-jl-a-fast-way-to-find-near-optimal-low-rank-approximations-of-kernel-matrices/138900)

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**Author:** [@Moblin88](https://discourse.julialang.org/u/Moblin88)\
**Replies:** 0\
**Last updated:** [August 18, 2026, 6:31pm UTC](https://discourse.julialang.org/t/ann-acceleratedrpcholesky-jl-a-fast-way-to-find-near-optimal-low-rank-approximations-of-kernel-matrices/138900 "2026-08-18T18:31:27Z")

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AcceleratedRPCholesky.jl for fast, near-optimal low-rank kernel matrix approximations I’m happy to announce AcceleratedRPCholesky.jl, which is an implementation of the Accelerated Randomly Pivoted Cholesky algorithm from…

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## [AOCL (not MKL) acceleration on AMD Ryzen CPU's](https://discourse.julialang.org/t/aocl-not-mkl-acceleration-on-amd-ryzen-cpus/112890)

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**Author:** [@aasdelat](https://discourse.julialang.org/u/aasdelat)\
**Replies:** 28\
**Last updated:** [August 10, 2026, 10:54am UTC](https://discourse.julialang.org/t/aocl-not-mkl-acceleration-on-amd-ryzen-cpus/112890 "2026-08-10T10:54:52Z")

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Hi: I am interested in calling a lapack routine, dgesvd, that makes a singular value decomposition of a matrix. The library LinearAlgebra.jl already does it, but it is a generic library that does not take full advantag…

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## [Hemiplex numbers and factoring symmetric indefinite matrices](https://discourse.julialang.org/t/hemiplex-numbers-and-factoring-symmetric-indefinite-matrices/138501)

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**Author:** [@tim.holy](https://discourse.julialang.org/u/tim.holy)\
**Replies:** 3\
**Last updated:** [July 29, 2026, 1:01pm UTC](https://discourse.julialang.org/t/hemiplex-numbers-and-factoring-symmetric-indefinite-matrices/138501 "2026-07-29T13:01:18Z")

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I’m pleased to announce the release of two new numeric packages, HemiplexNumbers and HemiplexFactorizations, and their accompanying manuscript Jordan algebras, hemiplex numbers, and the Cholesky decomposition of arbitrar…

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## [\[ANN\]: PhaseTypeDistributions.jl, PhaseTypeDistributionsFitting.jl (and FixedSparsityMatrices.jl)](https://discourse.julialang.org/t/ann-phasetypedistributions-jl-phasetypedistributionsfitting-jl-and-fixedsparsitymatrices-jl/137631)

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**Author:** [@yoninazarathy](https://discourse.julialang.org/u/yoninazarathy)\
**Replies:** 1\
**Last updated:** [June 25, 2026, 10:27am UTC](https://discourse.julialang.org/t/ann-phasetypedistributions-jl-phasetypedistributionsfitting-jl-and-fixedsparsitymatrices-jl/137631 "2026-06-25T10:27:55Z")

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We’re happy to announce two new packages for phase-type (PH) distributions, plus a supporting third package for structured matrices (which may be useful in its own right). A phase-type distribution is the distribution o…

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## [\[ANN\] GenLAProblems.jl — exact linear algebra exercise generators](https://discourse.julialang.org/t/ann-genlaproblems-jl-exact-linear-algebra-exercise-generators/137243)

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**Author:** [@ea42gh](https://discourse.julialang.org/u/ea42gh)\
**Replies:** 0\
**Last updated:** [May 22, 2026, 6:24pm UTC](https://discourse.julialang.org/t/ann-genlaproblems-jl-exact-linear-algebra-exercise-generators/137243 "2026-05-22T18:24:47Z")

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I’ve submitted GenLAProblems.jl for registration in General: GitHub - ea42gh/GenLAProblems.jl: Problem generator for standard linear algebra problems: creates problems with small integers and tractable computations · Gi…

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## [LAlatex.jl: feature requests for linear algebra display helpers?](https://discourse.julialang.org/t/lalatex-jl-feature-requests-for-linear-algebra-display-helpers/137080)

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**Author:** [@ea42gh](https://discourse.julialang.org/u/ea42gh)\
**Replies:** 1\
**Last updated:** [May 12, 2026, 4:14pm UTC](https://discourse.julialang.org/t/lalatex-jl-feature-requests-for-linear-algebra-display-helpers/137080 "2026-05-12T16:14:54Z")

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I recently registered LAlatex.jl v1.0.0 and am working on the next round of improvements. I’d appreciate feature requests from people using Julia for linear algebra in notebooks, teaching, examples, or generated LaTeX. R…

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## [Is the linear system solver \\ also multi threaded in Julia as in Matlab? And how to “multithread” it in Julia?](https://discourse.julialang.org/t/is-the-linear-system-solver-also-multi-threaded-in-julia-as-in-matlab-and-how-to-multithread-it-in-julia/47404)

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**Author:** [@nico](https://discourse.julialang.org/u/nico)\
**Replies:** 34\
**Last updated:** [May 1, 2026, 7:34am UTC](https://discourse.julialang.org/t/is-the-linear-system-solver-also-multi-threaded-in-julia-as-in-matlab-and-how-to-multithread-it-in-julia/47404 "2026-05-01T07:34:35Z")

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I am trying to compare speed and performance between Matlab and Julia. I am looking at a code that does topology optimization of a continuum structure subjected to a given load. The code I am looking at is the public cod…

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## [Creating and Solving Block Sparse Matrices with PETSc](https://discourse.julialang.org/t/creating-and-solving-block-sparse-matrices-with-petsc/90831)

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**Author:** [@Azurezaber](https://discourse.julialang.org/u/Azurezaber)\
**Replies:** 15\
**Last updated:** [April 27, 2026, 1:12pm UTC](https://discourse.julialang.org/t/creating-and-solving-block-sparse-matrices-with-petsc/90831 "2026-04-27T13:12:55Z")

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Hello! I am using Julia to write a finite volume CFD code, which requires solving large (40,000x40,000) block sparse matrices. Currently, I am using the PETSc interface provided by PETSc.jl, as its GMRES routine is notab…

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## [Julia analog to R's poly function, orthogonal polynomials by QR decomposition](https://discourse.julialang.org/t/julia-analog-to-rs-poly-function-orthogonal-polynomials-by-qr-decomposition/128640)

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**Author:** [@Daniel\_Johansson](https://discourse.julialang.org/u/Daniel_Johansson)\
**Replies:** 24\
**Last updated:** [April 22, 2026, 3:57pm UTC](https://discourse.julialang.org/t/julia-analog-to-rs-poly-function-orthogonal-polynomials-by-qr-decomposition/128640 "2026-04-22T15:57:18Z")

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Hey guys! Im trying to replicate some existing R code in julia for a proyect, but such R code depends on the stats base poly function which, given a collection of points, it computes orthogonal polynomials evaluated at …

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## [Argmax mapreduce on GPU](https://discourse.julialang.org/t/argmax-mapreduce-on-gpu/134971)

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**Author:** [@noetheriankoala](https://discourse.julialang.org/u/noetheriankoala)\
**Replies:** 6\
**Last updated:** [April 21, 2026, 9:35am UTC](https://discourse.julialang.org/t/argmax-mapreduce-on-gpu/134971 "2026-04-21T09:35:03Z")

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Hello! I am trying to quickly compute \\text{argmax}\_{\\substack{1 \\leq s \\leq k\\\\ k+1 \\leq t \\leq n}} A\_{s,t} + (1-\\ell\_s)(1 + \\ell\_t) I do this on the CPU with the following code. f = ((i, j),) -\> (i, j, A\[i, j\]^2 + …

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## [Solving linear systems without allocations, a comparison](https://discourse.julialang.org/t/solving-linear-systems-without-allocations-a-comparison/136193)

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**Author:** [@RobertGregg](https://discourse.julialang.org/u/RobertGregg)\
**Replies:** 6\
**Last updated:** [March 16, 2026, 10:49am UTC](https://discourse.julialang.org/t/solving-linear-systems-without-allocations-a-comparison/136193 "2026-03-16T10:49:42Z")

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I wanted to see how important removing allocations were when repeatedly solving linear systems (Ax=b), so I built a quick test package to try things out: GitHub - RobertGregg/QRLite.jl · GitHub. The interface uses FastLa…

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## [Numpy vs Julia matrix multiplication](https://discourse.julialang.org/t/numpy-vs-julia-matrix-multiplication/135992)

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**Author:** [@bernardofpc](https://discourse.julialang.org/u/bernardofpc)\
**Replies:** 7\
**Last updated:** [March 13, 2026, 7:42am UTC](https://discourse.julialang.org/t/numpy-vs-julia-matrix-multiplication/135992 "2026-03-13T07:42:30Z")

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I have performed two very simple tests in numpy and julia, and have obtained what I believe are significant differences in performance. This is on Windows 11, CPU: 28 × Intel(R) Core™ i7-14700. Numpy (python 3.12.7): I…

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## [\[ANN\] RecursiveFactorization.jl](https://discourse.julialang.org/t/ann-recursivefactorization-jl/39213)

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**Author:** [@YingboMa](https://discourse.julialang.org/u/YingboMa)\
**Replies:** 14\
**Last updated:** [February 13, 2026, 5:40pm UTC](https://discourse.julialang.org/t/ann-recursivefactorization-jl/39213 "2026-02-13T17:40:28Z")

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RecursiveFactorization allows you to perform any factorization you’d like so long as it is lu. If you like LU, DifferentialEquations.jl, or recursion, you’ll love RecursiveFactorization.jl. DifferentialEquations.jl use…

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## [Are there alternatives to Diagonal and eigvals compatible with Reactant?](https://discourse.julialang.org/t/are-there-alternatives-to-diagonal-and-eigvals-compatible-with-reactant/135081)

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**Author:** [@marcsgil](https://discourse.julialang.org/u/marcsgil)\
**Replies:** 13\
**Last updated:** [January 26, 2026, 3:22am UTC](https://discourse.julialang.org/t/are-there-alternatives-to-diagonal-and-eigvals-compatible-with-reactant/135081 "2026-01-26T03:22:02Z")

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Hello! I’m in the process of refactoring a complicated function so that it can be compiled by Reactant. It has not been very straightforward, but the speedup I’ve seen so far certainly justifies the effort. Nonetheless…

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## [Numerical sensitivity of eigvecs for \`≈\` identical (unitful) matrices?](https://discourse.julialang.org/t/numerical-sensitivity-of-eigvecs-for-identical-unitful-matrices/134846)

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**Author:** [@bremez](https://discourse.julialang.org/u/bremez)\
**Replies:** 3\
**Last updated:** [January 3, 2026, 2:11am UTC](https://discourse.julialang.org/t/numerical-sensitivity-of-eigvecs-for-identical-unitful-matrices/134846 "2026-01-03T02:11:09Z")

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I came across the following discrepancy, see MWE: using LinearAlgebra, Unitful GHz = 1u"GHz"; wq = 6.7565\*GHz; wc = 20\*GHz; g = 0.1847\*GHz; Ns = 10; op = diagm(1 =\> sqrt.(1:Ns)); b = kron(op, I(Ns+1)); a = kron(I(Ns+1),…

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## [Eigenvectors with the most overlap with v](https://discourse.julialang.org/t/eigenvectors-with-the-most-overlap-with-v/134008)

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**Author:** [@Nichola](https://discourse.julialang.org/u/Nichola)\
**Replies:** 7\
**Last updated:** [December 18, 2025, 1:39am UTC](https://discourse.julialang.org/t/eigenvectors-with-the-most-overlap-with-v/134008 "2025-12-18T01:39:40Z")

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Given a sparse matrix M and a vector v, I would like to get the k eigenvectors of M that have the most overlap with v. Is there an efficient method for doing this with sparse matrices ? All sparse solvers I ran into tar…

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## [GEMM kernel, cache oblivious, and Strassen](https://discourse.julialang.org/t/gemm-kernel-cache-oblivious-and-strassen/126527)

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**Author:** [@photor](https://discourse.julialang.org/u/photor)\
**Replies:** 5\
**Last updated:** [November 19, 2025, 5:18am UTC](https://discourse.julialang.org/t/gemm-kernel-cache-oblivious-and-strassen/126527 "2025-11-19T05:18:07Z")

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I think many people are curious about how a GEMM kernel written in pure Julia can be much more performant than a naively written one. One can inspect the source code of LoopVectorization.jl, of course, or even the more p…

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## [Linear Algebra Manipulations with Cholesky Factors](https://discourse.julialang.org/t/linear-algebra-manipulations-with-cholesky-factors/133899)

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**Author:** [@gideonsimpson](https://discourse.julialang.org/u/gideonsimpson)\
**Replies:** 1\
**Last updated:** [November 15, 2025, 6:51pm UTC](https://discourse.julialang.org/t/linear-algebra-manipulations-with-cholesky-factors/133899 "2025-11-15T18:51:20Z")

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I’m working on a problem where I need to do some Gaussian random variable sampling, which would naive be implemented as: nx = 10 e = ones(nx) A = spdiagm(-1 =\> -e\[1:end-1\], 0 =\> 2e, 1 =\> -e\[1:end-1\]) chol = cholesky(A, …

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## [Solving Projection onto Linear Equality for Multiple Input Vectors](https://discourse.julialang.org/t/solving-projection-onto-linear-equality-for-multiple-input-vectors/133428)

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**Author:** [@RoyiAvital](https://discourse.julialang.org/u/RoyiAvital)\
**Replies:** 11\
**Last updated:** [October 31, 2025, 8:52pm UTC](https://discourse.julialang.org/t/solving-projection-onto-linear-equality-for-multiple-input-vectors/133428 "2025-10-31T20:52:18Z")

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I am after solving the projection onto a Linear Equation problem: \\arg \\min\_{\\boldsymbol{x}} \\frac{1}{2} {\\left\\| \\boldsymbol{x} - \\boldsymbol{y} \\right\\|}\_{2}^{2} \\; \\text{ subject to } \\boldsymbol{A} \\boldsymbol{x} =…

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## [Batched Matrix Multiply](https://discourse.julialang.org/t/batched-matrix-multiply/42332)

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**Author:** [@bmit](https://discourse.julialang.org/u/bmit)\
**Replies:** 12\
**Last updated:** [October 30, 2025, 8:22am UTC](https://discourse.julialang.org/t/batched-matrix-multiply/42332 "2025-10-30T08:22:15Z")

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I’d like to be able to be able to broadcast matrix multiplication across multidimensional arrays similar to the following: a = rand(4,3,2) b = rand(3,4,2) a .\* b # expect a (4,4,2) array, but instead errors I underst…

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## [Non reproducible result - Linear algebra](https://discourse.julialang.org/t/non-reproducible-result-linear-algebra/132986)

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**Author:** [@Maucejo](https://discourse.julialang.org/u/Maucejo)\
**Replies:** 8\
**Last updated:** [October 9, 2025, 10:52am UTC](https://discourse.julialang.org/t/non-reproducible-result-linear-algebra/132986 "2025-10-09T10:52:31Z")

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Hi all, I am implementing some algorithms for modal parameters extraction for the next release of StructuralVibration.jl. One of the method implemented is the Least-Squares Complex Frequency method (LSCF). The code ofte…

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## [Updating the QR decomposition of a matrix under rank-1updates](https://discourse.julialang.org/t/updating-the-qr-decomposition-of-a-matrix-under-rank-1updates/132831)

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**Author:** [@Gattu\_Mytraya](https://discourse.julialang.org/u/Gattu_Mytraya)\
**Replies:** 3\
**Last updated:** [October 3, 2025, 12:47am UTC](https://discourse.julialang.org/t/updating-the-qr-decomposition-of-a-matrix-under-rank-1updates/132831 "2025-10-03T00:47:05Z")

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Hi, I was trying to find a native julia implementation of the QR decomposition of a matrix A when it is changed from A to A + uv^{T} - under a rank-1 update. I found multiple packages for updating the QR decomp (and jus…

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## [Solving Optimization of Least Squares Term with Quadratic Term with Memory Infeasible Matrix](https://discourse.julialang.org/t/solving-optimization-of-least-squares-term-with-quadratic-term-with-memory-infeasible-matrix/132599)

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**Author:** [@RoyiAvital](https://discourse.julialang.org/u/RoyiAvital)\
**Replies:** 2\
**Last updated:** [September 24, 2025, 2:41pm UTC](https://discourse.julialang.org/t/solving-optimization-of-least-squares-term-with-quadratic-term-with-memory-infeasible-matrix/132599 "2025-09-24T14:41:15Z")

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I want to solve: \\arg \\min\_{\\boldsymbol{x}} \\frac{\\lambda}{2} \\boldsymbol{x}^{T} \\boldsymbol{E}^{T} \\boldsymbol{K} \\boldsymbol{E} \\boldsymbol{x} + \\frac{\\rho}{2} {\\left\\| \\boldsymbol{A} \\boldsymbol{x} - \\boldsymbol{y} …

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## [Large Sparse Hermitian Matrix - Intermediate Eigenvalue Problem](https://discourse.julialang.org/t/large-sparse-hermitian-matrix-intermediate-eigenvalue-problem/131600)

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**Author:** [@Neilis](https://discourse.julialang.org/u/Neilis)\
**Replies:** 9\
**Last updated:** [September 23, 2025, 2:22pm UTC](https://discourse.julialang.org/t/large-sparse-hermitian-matrix-intermediate-eigenvalue-problem/131600 "2025-09-23T14:22:14Z")

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Hi, I am trying to find eigenvalues and eigenvectors for a rather large, sparse, hermitian matrix (size ~1E7 x 1E7). I am mainly interested in around 40 eigenvalues in the middle of the spectrum. To solve this original…

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## [\`map\` should be more consistent](https://discourse.julialang.org/t/map-should-be-more-consistent/132559)

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**Author:** [@WalterMadelim](https://discourse.julialang.org/u/WalterMadelim)\
**Replies:** 7\
**Last updated:** [September 23, 2025, 1:31am UTC](https://discourse.julialang.org/t/map-should-be-more-consistent/132559 "2025-09-23T01:31:32Z")

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Dear all, I wonder if it is proper to amend this behavior? julia\> map(\_ -\> 0, 0) 0 julia\> struct Nvmber end julia\> Base.ndims(::Nvmber) = 0 julia\> Base.length(::Nvmber) = 1 julia\> Base.iterate(f::Nvmber) = (f, miss…

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## [Apple M4 Max AMX Linear Algebra performance versus CPU and GPU](https://discourse.julialang.org/t/apple-m4-max-amx-linear-algebra-performance-versus-cpu-and-gpu/132537)

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**Author:** [@PetarM](https://discourse.julialang.org/u/PetarM)\
**Replies:** 2\
**Last updated:** [September 22, 2025, 12:17am UTC](https://discourse.julialang.org/t/apple-m4-max-amx-linear-algebra-performance-versus-cpu-and-gpu/132537 "2025-09-22T00:17:46Z")

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Hello everybody! I made a video investigation of Apple’s AMX accelerator Linear Algebra performance in Julia: https://www.youtube.com/watch?v=TjfA9LVgHXk According to my findings, the 2 AMX cores achieve almost 3 times…

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## [How to update a symmetric matrix respecting API boundaries?](https://discourse.julialang.org/t/how-to-update-a-symmetric-matrix-respecting-api-boundaries/132246)

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**Author:** [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Replies:** 8\
**Last updated:** [September 11, 2025, 4:23pm UTC](https://discourse.julialang.org/t/how-to-update-a-symmetric-matrix-respecting-api-boundaries/132246 "2025-09-11T16:23:22Z")

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Suppose I have a symmetric matrix H, and I would like to update it in place. For the purposes of this MWE, the update is adding f(i,j) to elements, based on index. How can I do this while respecting API boundaries? seti…

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