# 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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### General

- 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 speedÂ with large sizes based on the IntelÂ® Math Kernel Library.
- Native 64-bit support.

### Vectors

- 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.)

### Matrices

- 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.