numpy

NumPy → .NET

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.

NumPy need	Recommended .NET
Vectors/matrices, decompositions, linear solves	Math.NET Numerics (MathNet.Numerics), + native MKL/OpenBLAS provider for performance
Element-wise vectorized ops (SIMD)	System.Numerics.Tensors (TensorPrimitives)
"NumPy-like" API (migration comfort)	NumSharp — handy, but less mature; reserve for porting convenience

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

Pitfalls

• 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.