Verdict: use what exists. NumPy's dense algebra relies on BLAS/LAPACK; we don't rewrite that. We combine two .NET building blocks as needed.

Two decompositions are the exception, and they ship here. The row above still holds for a general dense linear-algebra need — Math.NET is the answer for a solve, an eigendecomposition or a full SVD of a dense matrix. It is not the answer for a sparse truncated SVD or for non-negative matrix factorization, which Lodestar.Decomposition writes natively over a CsrMatrix at scikit-learn parity: Math.NET 5.0.0 dates from April 2022 and has shipped nothing but a beta in the four years since, its sparse SVD request has been open since 2013, and densifying a term-document matrix to reach Svd() is the cost the sparse representation existed to avoid. See docs/guides/decomposition.md.

You do not have to choose one side. Lodestar.Extensions.MathNet converts a CsrMatrix to and from Math.NET's SparseMatrix in one pass over the stored values, so a matrix can be vectorized and factorized here and then solved, inverted or eigendecomposed there — without a densify-and-rebuild round trip in between. It is the only package in this repository that references Math.NET, and it references it to convert to it rather than to compute with it, which is why the paragraph above still stands (decision 0003).

dotnet add package Lodestar.Extensions.MathNet

dotnet add package MathNet.Numerics
dotnet add package MathNet.Numerics.MKL.Win-x64   # or .Linux-x64: native acceleration

using MathNet.Numerics.LinearAlgebra;

var a = Matrix<double>.Build.DenseOfArray(new[,] { { 1.0, 2.0 }, { 3.0, 4.0 } });
var b = Vector<double>.Build.Dense(new[] { 1.0, 1.0 });
Vector<double> x = a.Solve(b);   // solves a·x = b

• Broadcasting. No universal implicit equivalent: write it explicitly, or use TensorPrimitives for element-wise work.
• dtype / views. Math.NET is strongly typed (double, float, Complex); no zero-cost views like NumPy — slices often copy.
• Randomness. MathNet.Numerics.Random ≠ NumPy generators: don't expect cross-reproducible draws.

Guide to be expanded as real needs arise.