C++ Implementation of A Linear Algebra Library

• LINear ALGebra library
  • Overview
  • Usage
  • References

This library contains a basic implementation of three different classes on the real numbers domain: Polynomial, Vector and Matrix. Here, a brief overview of the functionalities for each kind of object is provided. To have a more precise idea of all the available methods just have a look to the header file linalg.hpp.

• Polynomial

  • basic algebraic operations (addition, subtraction, multiplication and division)
  • evaluation in a specific point
  • evaluation of the derivative in a specific point
  • computation of the zeros (if all real)

• Vector

  • basic algebraic operations (addition, subtraction)
  • multiplication by a scalar
  • Hadamard product (element-wise)
  • dot product
  • outer product
  • computation of the Lp norm (default: L2)
  • projection onto another Vector

• Matrix

  • basic algebraic operations (addition, subtraction)
  • multiplication by a scalar
  • matrix multiplication
  • computation of the norm (L2, nuclear, default: Frobenius)
  • transposition
  • gaussian elimination
  • inversion
  • determination of the rank
  • computation of the trace
  • computation of the determinant by different methods (Laplace, default: Gauss)
  • eigendecomposition (only for symmetric matrices)
  • singular values decomposition (SVD) for rectangular matrices
  • QR decomposition
  • Cholesky decomposition for positive definite matrices
  • LU decomposition
  • computation of the characteristic Polynomial

• Others

  • dot product between Matrix and Vector
  • Gram-Schmidt orthonormalization
  • 1D convolution between vectors
  • 2D convolution between matrices

First of all, you have to clone the repository and change directory:

git clone https://github.com/ryandoren/Linalg.git
cd linalg

Then, you can easily build the linalg library (on Linux system only) using CMake:

cmake .
make

Finally, you can run as an example the executable example.out simply typing:

./example.out