linalg

A personal project that implements matricies, vectors, matrix operations, and other linear algebra topics in Python.

Creating a Matrix

• m*n matrix -> Matrix(m, n)
• n*n identity matrix -> Matrix(n, "identity")

Supported Functions on Matrices

• Addition -> A+B, where A and B are both m*n matrices (returns a new object)
• Multiplication -> A*B, where A is an m*n matrix, and B is an n*p matrix (returns a new object)
• Copy -> A.copy() (returns a new object)
• Get -> A.get(i, j), returns the value of the matrix entry at (i, j)
• Set -> A.set(i, j, x), sets the matrix entry at (i, j) to the value x
• Get Column Vector -> A.get_vector(n), returns the vector at column n
• Transpose -> A.transpose(), transposes the current matrix object
• Symmetric? -> A.is_symmetric(), returns whether a matrix is symmetric
• Gauss Elimination -> A.gauss(), performs standard Gaussian Elimination on the current matrix object (returns true if an odd amount of row swaps are made, false if even amount of row swaps are made)
• Rank -> A.rank(), returns the rank (number of pivots) of the current matrix object
• Reduced Row Echelon Form -> A.rref(), brings the current matrix object to its reduced row echelon form
• Inverse -> A.inverse(), inverts the current matrix object (if invertible)
• Determinant -> A.det(), returns the determinant of the current matrix object
• Projection Matrix -> A.proj_matrix(), returns the projection matrix of the current matrix object
• Projection -> A.proj(b), returns the projection of vector b onto the current matrix object