Python Module that contains functions for matrix operations and theoretical interpretations in Linear Algebra (ranging from basic matrix algebra to determinants, vector spaces, and eigenvalues/vectors)
move the module MatrixOperations.py into your working directory and import it into the file of your choosing
import MatrixOperationsLibrary as molHere is the list of functions that the module currently contains:
| Function | Description |
|---|---|
| loadMatrix | reads matrix in from file and returns it as a 2D array |
| numCols | returns the number of columns for a specified matrix |
| numRows | returns the number of rows for a specified matrix |
| transpose | returns a matrix with the rows and columns swapped |
| isVector | returns whether or not the given matrix is a vector (1 dimensional) |
| isSquare | returns whether not the given matrix is square |
| identity | returns an identity matrix of specified size |
| add | adds two matrices |
| subtract | subtracts two matrices |
| scale | multiplies a given matrix with a scalar value |
| dot | dot product of two vectors |
| cross | cross product of two vectors |
| multiply | matrix product of two matrices |
| elementPower | raises each element of a matrix to a specified power |
| power | raises a given matrix to the given power (multiplying the matrix by itself n times where n is the given power) |
| swap | swaps two specified rows of a matrix |
| pivot | returns the indices of the first pivot position after ths given index |
| upperTriangle | returns a tuple of the given matrix in upper triangular form and the number of row interchanges |
| echelon | row reduces a given matrix to echelon form |
| reducedEchelon | row reduces a given matrix to reduced row echelon form (RREF) |
| augment | combines a coeffecient matrix and an answer vector into an augmented matrix |
| linearDependence | returns whether or not the columns of the given matrix are linearly dependent (boolean) |
| submatrix | given an n by n matrix and a row and column index, returns a n-1 by n-1 submatrix disregarding the specified row/column |
| determinant | finds the determinant of a given matrix |
| recursiveDeterminant | finds the determinant of a given matrix recursively |
| inverse | returns the inverse of a given matrix |
| gaussianSolve | using Gaussian elimination, solves the equation Ax = b for the x vector, where A is a given coeffecient matrix and b is a given answer vector. This function will determine if a system is inconsistent or return a dictionary where each key (const, x1, x1, x2, etc.) will have a vector as its value (this represents the Parametric Vector Form of the solution). |
| inverseSolve | using the property of matrix invertability, solves the equation Ax = b for the x vector, where A is a given coeffecient matrix and b is a given answer vector |
| cramersSolve | using Cramer's Rule, solves the equation Ax = b for the x vector, where A is a given coeffecient matrix and b is a given answer vector |
| nullSpace | returns the null space of a given matrix A as a dictionary (solution to Ax=0 using gaussianSolve()) |
| colSpace | return the column space of a given matrix A as a dictionary |