Matrix-Library (C++)

A comprehensive, template-based C++ matrix algebra library inspired by MIT OpenCourseWare 18.06 (Linear Algebra). It supports common matrix operations plus higher-level linear-algebra algorithms such as Gaussian elimination, LU/QR factorization, SVD, least-squares fitting, eigen computations, and FFT utilities. It also supports complex matrices.

Features

Matrix class (template)

• Template matrix type: matrix<DataType> (works with int, float, double, long double, and the included complex)
• Basic operations
  • Addition/subtraction: operator+, operator-
  • Matrix multiply/divide: operator*, operator/ (division uses inverse)
  • Scalar multiply: operator*(DataType)
  • Power: operator^(power)
  • Transpose: transpose()
  • Dot product: dot()
• Matrix properties
  • det(), trace(), rank()
  • is_square(), same_shape(), operator==
  • Feature checks: is_symmetric(), is_identity(), is_zero(), is_diagonal(), is_upper_tri(), is_lower_tri(), is_orthogonal(), etc.
• Solvers / factorizations / advanced algorithms
  • Gaussian elimination: gauss_down(), gauss_up(), rref()
  • LU: lu_fact(L, P, U)
  • QR: qr_fact(Q, R)
  • SVD: svd(U, S, VT)
  • Inverse: inverse()
  • Linear system solve (augmented matrix): solve()
  • Least squares: fit_least_squares(output)
  • Projection matrix: projection()
  • Gram–Schmidt: gram_shmidt()
  • Eigenvalues / eigenvectors: eigen_values(max_iteration, min_diff), eigen_vectors(eigen_values)
• FFT
  • fft_col(dimension), fft()
  • Fourier helpers: fourier_diagonal(), fourier_mat()

Matrix type detection & compression

The library can detect special matrix structures and store them more efficiently:

• Types include: general, utri, ltri, diagonal, symmetric, anti_symmetric, constant, iden, orthonormal
• Methods:
  • fill_features(check_tol)
  • compress()
  • decompress()

Complex numbers

Includes a custom complex number type in complex.h / complex.cpp supporting:

• Arithmetic operators, scalar ops, power ^, comparisons, polar angle theta()
• Helper functions like abs(), conjugate(), etc.
• Complex matrices are supported with their operations (hermitian inner product)

Repository layout

• matrix_algebra.h / matrix_algebra.cpp — main matrix library
• complex.h / complex.cpp — complex number implementation
• DOCUMENTATION.MD — detailed API/feature documentation
• DEMO.md — demo link
• README.md — (this file)

Getting started

1) Include the headers

#include "matrix_algebra.h"
#include <iostream>
using namespace std;

2) Example usage

#include "matrix_algebra.h"
#include <iostream>

using namespace std;

int main() {
    matrix<double> A(3, 3);
    matrix<double> B(3, 3);

    A.fill(2.0);
    B.set_identity();

    matrix<double> C = A + B;
    matrix<double> D = A * B;

    cout << "det(A) = " << A.det() << "\n";
    cout << "rank(A) = " << A.rank() << "\n";

    matrix<double> invA = A.inverse();

    // Solve Ax = b using appended matrix [A|b]
    matrix<double> b(3, 1);
    b.fill(1.0);
    matrix<double> Ab = A.append_cols(b);
    matrix<double> x = Ab.solve();

    A.show();
    return 0;
}

Notes / behavior

• Indexing is 0-based (at(row, col)).
• Some operations return “error values” (e.g., -1 or a matrix(1,1,-1)) when shapes are invalid or a square matrix is required.
• compress() can reduce storage for special matrix types; operations are intended to work with both compressed and uncompressed matrices.

Demo

See DEMO.md for the YouTube demo link.

Documentation

For the full list of functions and explanations, see DOCUMENTATION.MD.