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Algebracha 🌶

A Python library adding support for basic Linear Algebra and Analytic Geometry operations

Creating a new matrix object

from algebracha import Matrix

matrix = Matrix('1 2 3, 4 5 6')

Matrix's constructor requires one string argument that defines the actual matrix:
EG: to create the following matrix:

1 2 3 4
5 6 7 8

The argument string must be:

'1 2 3 4, 5 6 7 8'

# or

'''
  1 2 3 4,
  5 6 7 8
'''

Methods

matrix = Matrix('1 2 3, 4 5 6, 7 8 9)

Compute determinant

Returns the determinant of the matrix

matrix.determinant()

Check if the matrix is square

Returns True if the matrix is square, False otherwise

matrix.isSquare()

Check if the matrix is diagonal

Returns True if the matrix is diagonal, False otherwise. Matrix must be square

matrix.isDiagonal()

Check if matrix is equal to another matrix

Returns True if the matrix passed as argument is equal to this matrix, False otherwise
otherMatrix = Matrix('1 2, 3 4')
matrix.equals(otherMatrix)

Operations

Transpose matrix

Transposes the matrix

matrix.transpose()

Sum matrices

Sums the matrix passed as argument with this matrix
otherMatrix = Matrix('1 2, 3 4')
matrix.sum(otherMatrix)

Multiply matrices

Multiply this matrix with the matrix passed as argument using the "row by column" method
otherMatrix = Matrix('1 2, 3 4, 5 6, 7 8')
matrix.sum(otherMatrix)

Swap rows

Swap two rows
matrix.swapRows(1, 2) #row count starts at 1

Swap columns

Swap two columns
matrix.swapColumns(1, 2) #column count starts at 1

Sum rows

Sum two rows
matrix.sumRows(1, 2)    #row 1 becomes the sum of row 1 and row 2
matrix.sumRows(1, 2, 2) #row 1 becomes the sum of row 1 and row 2 multiplied by 2

Sum columns

Sum two columns
matrix.sumColumns(1, 2)    #column 1 becomes the sum of column 1 and column 2
matrix.sumColumns(1, 2, 2) #column 1 becomes the sum of column 1 and column 2 multiplied by 2

Multiply row elements by a scalar

Arguments: row index, scalar
matrix.multiplyRow(1, 3)

Multiply column elements by a scalar

Arguments: column index, scalar
matrix.multiplyColumn(2, 4)

Compute rank of the matrix

Get the max number of linarly independent rows or columns
matrix.rank()

Transform matrix to its echelon form

Transform to echelon form using Gaussian Elimination
matrix.transformEchelon()

Solve system of linear equations

Compute the solutions of the linear system associated to the matrix
Example:

Linar system to matrix form:

3 -5 1 0
3 6 -5 1
2 -7 4 4 
matrix = Matrix('''
  3 -5 1 0,
  3 6 -5 1,
  2 -7 4 4
''')

matrix.solveSystem()

returns array of solutions: [x, y, z]

[1.348, 0.515, 1.227]

Compute inverse matrix

Returns the inverse matrix
matrix.getInverse()