Vector and Matrix Library Features

Below is a list of features for the vector and matrix library portion of Extreme Numerics.NET. Also see the detailed math, statistics, and data analysis feature lists.

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  • Single, double, or quad precision real or complex components.
  • Based on standard BLAS and LAPACK routines.
  • 100% managed implementation for security, portability and small sizes.
  • Native, processor-optimized implementation for speed with large sizes based on the Intel® Math Kernel Library.
  • Native 64-bit support.


  • Dense vectors.
  • Band vectors.
  • Constant vectors.
  • Row, column and diagonal vectors.
  • Vector views.

Vector Operations

  • Basic arithmetic operations.
  • Element-wise operations.
  • Overloaded arithmetic operators.
  • Norms, dot products.
  • Largest and smallest values.
  • Functions of vectors (sine, cosine, etc.)


  • General matrices.
  • Triangular matrices.
  • Real symmetric matrices and complex Hermitian matrices.
  • Band matrices.
  • Diagonal matrices.
  • Matrix views.

Matrix Operations

  • Basic arithmetic operations.
  • Matrix-vector products.
  • Overloaded arithmetic operations.
  • Element-wise operations.
  • Row and column scaling.
  • Norms, rank, condition numbers.
  • Singular values, eigenvalues and eigenvectors.

Matrix Decompositions

  • LU decomposition.
  • QR decomposition.
  • Cholesky decomposition.
  • QL, LQ, QR decompositions.
  • Symmetric eigenvalue decomposition.
  • Non-symmetric eigenvalue decomposition.
  • Generalized eigenvalue decomposition.
  • Singular value decomposition.
  • Generalized singular value decomposition.
  • Banded LU and Cholesky decomposition.
  • Non-negative matrix factorization (NMF) - Coming soon!

Sparse Matrices

  • Sparse vectors
  • Sparse matrices
  • Matrices in Compressed Sparse Column format
  • Sparse LU and Cholesky Decomposition
  • Read matrices in Matrix Market format

Linear equations and least squares

  • Shared API for matrices and decompositions.
  • Determinants, inverses, numerical rank, condition numbers.
  • Solve equations with one or multiple right-hand sides.
  • Least squares solutions using QR or Singular Value Decomposition.
  • Moore-Penrose Pseudo-inverse.
  • Non-negative least squares (NNLS)

GPU computing

  • GPU computing: offload computations to the GPU.
  • Data is kept on the GPU as long as possible for optimal performance.