Kabanosk / lin-algebra

Documentation of package lin_algebra

This is the documentation of a package named lin-algebra. This package includes a function which can help with many linear algebra problems.
Copyright (c) 2021 Wojciech Fiołka

lin-algebra.Matrix

Constructor

Take a two-dimensional list as a parameter and make a Matrix object.

Operators overloaded

• (+) add two matrices and return a Matrix object with added elements.
• (-) subtract two matrices and return a Matrix object with subtracted elements.
• (* num) (type float or int) multiply all elements of Matrix by the number.
• (* Matrix) make matrix multiplication and return the Matrix object of it.
• (+=) add each element of the called Matrix to the corresponding element.
• (-=) subtract each element of the called Matrix by corresponding element.
• (*= num) (type float or int) multiply all elements of the called Matrix by the number.
• (*= Matrix) make matrix multiplication and change called Matrix to the result of it.
• (==) return true if all elements are the same.
• (!=) return true if it is the difference between two matrices.

Operations on matrices

• det() return determinant of the squared matrix.
• is_squared() return true if the matrix is squared and false if it is not.
• T() return a Matrix objets which is the transpose of the called matrix.
• inv() return a Matrix object which is inverse of the called matrix.

Operations on the diagonal and antidiagonal

• is_diagonal() return if the called matrix is diagonal.
• get_main_diagonal() return list includes elements of main diagonal.
• is_identity() return if the called matrix is identity.
• is_antidiagonal() return if the called matrix is anti-diagonal.
• get_antidiagonal() return list includes elements of antidiagonal.
• is_exchange() return if the called matrix is exchanged.
• trace() return trace of diagonal matrix.

Other functions

• size() return tuple with number of rows and columns.
• print() print matrix.
• gen_zero(rows, columns) return Matrix objects with size specified by rows and columns.
• gen_random(rows, columns) return Matrix objects with size specified by rows and columns.

lin-algebra.Vector

Constructor

Take as parameter one-dimensional list and create Vector object

Overloaded operators

• (+) add two vectors and return a Vector object with added elements.
• (-) subtract two vectors and return a Vector object with subtracted elements.
• (* num) (type float or int) multiply all elements of Vector by the number.
• (* Vector) make a dot product and return the result of it.
• (+=) add to each element of the called Vector the corresponding element.
• (-=) subtract each element of the called Vector by corresponding element.
• (*= num) (type float or int) multiply all elements of the called Vector by the number.
• (*= Vector) make a dot product and change the called Vector to the result of it.
• (==) return true if all elements are the same.
• (!=) return true if it is the difference between two vectors.

Operations on vectors

• vector_scalar_product(scalar) multiply each element by scalar and return the new vector
• dot(V1) return dot product of vectors
• cross(V1) return tuple includes Vector object with elements created by cross product and length of the result vector

Other functions

• size() return the size of the Vector.
• length() return the length of the Vector.
• print() prints vector.
• gen_zero(dimensions) return Vector object of zero vector
• gen_random(dimensions) return Vector object with random values from 0 to 30