Linear-Algebra-Package

Multidimensional array (Matrix)

A matrix is table of numbers, expressions and other data, arranged with index or coordinates, the size corresponds to the dimension and it's m rows and n columns, matrices have defined differents operations between them.

A matrix with same number of columns that rows is a square matrix.
A matriz with 1 row and n columns is a row vector for n dimension.
A matrix with 1 column and m rows is a column vector for m dimension.

For create a matrix this package have a class called Matrix that use the list objects to define them, and have two ways to create matrices. For example you can create nested lists objects, that represent de number of rows and append the elements for each row and that number of elements is the number of columns.

m = Matrix([[1, 2, 3], [4, 5, 6], [6, 7, 8]])

It class take 1 positional argument that is the nested list.

m = Matrix([1, 2, 3], [4, 5, 6], [6, 7, 8])#WRONG
m = Matrix(1,2,3,4,5,6,7,8)#WRONG

Other way to create a matrix is from her values, it method use n arguments for matrix elements and 2 positional arguments that should be the number of rows and the number of columns.

m = Matrix.from_values(1, 2, 3, 4, 5, 6, dim_m=2, dim_n=3)

Matrix with 1 row or column (Vector)

For create a vector the package have a class that inherence from Matrix that is Vector is similar to Matrix object but with other atributes. For example you can create a lists with the values of the vector.

v = Vector([2, 2, 0])# row vector

v = Vector(2, 2, 0)#WRONG
v = Vector([[2, 2, 8]])#WRONG

Other way to create vector from a Matrix object, that takes the first row of the matrix.

v = Vector.from_matrix([[2, 2, 0]])

For create columns vectors is create row vector and apply .transposed() method.

v = Vector([2, 2, 0]).transposed()# col vector

Operations

Addition and Subtraction

For add or sustract matrices, they should have the same dimention mxn and for do this you can use the + and - operator in Matrix object.

m = Matrix([[0, -3, 4], [3, 0, 0], [-4, 0, 0]])
print(m+m)
print(m-m)

Scalar Product

This operation multiply a real number C with a matrix, each element in the matrix is multiply for C.

For multiply you can use scalar_mul() that recive 1 possitional argument.

m = Matrix([[0, -3, 4], [3, 0, 0], [-4, 0, 0]])
m.scalar_mul(2)

Transposition

Is transform a mxn matrix in nxm matrix, turning the rows anf the columns

m = Matrix([[0, -3, 4], [3, 0, 0], [-4, 0, 0]])
m.transposed()

Matrix multiplication and power

For operate two matrices, left one should have the same number of columns that rows of the right one

  m1 = Matrix([[1, 2, 3], [4, 5, 6], [6, 7, 8]])
  m2 = Matrix([[1, 2, 3], [2, 3, 4], [5, 6, 7], [8, 9, 10]])
  m3 = m2*m1

For power operation is do multiplication with same matrix but they must have the same number of rows that columns, we can use two forms first do multiplication of m*m after that result *m or only use pow python operator.

  m = Matrix([[1, 2, 3], [4, 5, 6], [6, 7, 8]])
  m3 = (m*m)*m
  m2 = m**2

xhapa/Linear-Algebra-Package