Multiplication with Matrices

scalar_product_matrix(matrix, scalar)

Calculates the product of a matrix and a scalar

Parameters

  • matrix (list of lists of int or float) – List of lists of numbers representing a matrix

  • scalar (int or float) – Number representing a scalar

Raises

  • TypeError – First argument must be 2-dimensional lists

  • TypeError – Elements nested within first argument must be integers or floats

  • TypeError – Second argument must be an integer or a float

Returns

matrix – List of lists in which each inner element is the product of the corresponding element from the input matrix and the scalar value

Return type

list of lists of int or float

See also

scalar_product_vector(), matrix_sum()

Notes

  • Matrix: \(\mathbf{A} = \begin{bmatrix} a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\ a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\ \cdots & \cdots & \cdots & \cdots \\ a_{m,1} & a_{m,2} & \cdots & a_{m,n} \end{bmatrix}\)

  • Scalar: \(c\)

  • Scalar product: \(c\cdot{\mathbf{A}} = \begin{bmatrix} c\cdot{a_{1,1}} & c\cdot{a_{1,2}} & \cdots & c\cdot{a_{1,n}} \\ c\cdot{a_{2,1}} & c\cdot{a_{2,2}} & \cdots & c\cdot{a_{2,n}} \\ \cdots & \cdots & \cdots & \cdots \\ c\cdot{a_{m,1}} & c\cdot{a_{m,2}} & \cdots & c\cdot{a_{m,n}} \end{bmatrix}\)

  • Matrix Multiplication with Scalars

Examples

Import scalar_product_matrix function from regressions library
>>> from regressions.matrices.multiplication import scalar_product_matrix
Multiply [[1, 2, 3], [4, 5, 6]] and -2
>>> matrix_2x3 = scalar_product_matrix([[1, 2, 3], [4, 5, 6]], -2)
>>> print(matrix_2x3)
[[-2, -4, -6], [-8, -10, -12]]
Multiply [[5, -7], [-3, 8]] and 3
>>> matrix_2x2 = scalar_product_matrix([[5, -7], [-3, 8]], 3)
>>> print(matrix_2x2)
[[15, -21], [-9, 24]]
matrix_product(matrix_one, matrix_two)

Calculates the product of two matrices

Parameters

  • matrix_one (list of lists of int or float) – List of lists of numbers representing a matrix

  • matrix_two (list of lists of int or float) – List of lists of numbers representing a matrix

Raises

  • TypeError – Arguments must be 2-dimensional lists

  • TypeError – Elements nested within arguments must be integers or floats

  • ValueError – First list within first argument must contain the same amount of elements as the amount of lists contained within second argument

Returns

matrix – List of lists in which each inner element is the dot product of the first matrix’s row vector corresponding to that element’s row position and the second matrix’s column vector corresponding to that element’s column position; resultant matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix

Return type

list of lists of float

See also

dot_product(), transposed_matrix()

Notes

  • First matrix: \(\mathbf{A} = \begin{bmatrix} a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\ a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\ \cdots & \cdots & \cdots & \cdots \\ a_{m,1} & a_{m,2} & \cdots & a_{m,n} \end{bmatrix}\)

  • Second matrix: \(\mathbf{B} = \begin{bmatrix} b_{1,1} & b_{1,2} & \cdots & b_{1,p} \\ b_{2,1} & b_{2,2} & \cdots & b_{2,p} \\ \cdots & \cdots & \cdots & \cdots \\ b_{n,1} & b_{n,2} & \cdots & b_{n,p} \end{bmatrix}\)

  • Product of matrices: \(\mathbf{A}\cdot{\mathbf{B}} = \begin{bmatrix} a_{1,1}\cdot{b_{1,1}} + a_{1,2}\cdot{b_{2,1}} + \cdots + a_{1,n}\cdot{b_{n,1}} & a_{1,1}\cdot{b_{1,2}} + a_{1,2}\cdot{b_{2,2}} + \cdots + a_{1,n}\cdot{b_{n,2}} & \cdots & a_{1,1}\cdot{b_{1,p}} + a_{1,2}\cdot{b_{2,p}} + \cdots + a_{1,n}\cdot{b_{n,p}} \\ a_{2,1}\cdot{b_{1,1}} + a_{2,2}\cdot{b_{2,1}} + \cdots + a_{2,n}\cdot{b_{n,1}} & a_{2,1}\cdot{b_{1,2}} + a_{2,2}\cdot{b_{2,2}} + \cdots + a_{2,n}\cdot{b_{n,2}} & \cdots & a_{2,1}\cdot{b_{1,p}} + a_{2,2}\cdot{b_{2,p}} + \cdots + a_{2,n}\cdot{b_{n,p}} \\ \cdots & \cdots & \cdots & \cdots \\ a_{m,1}\cdot{b_{1,1}} + a_{m,2}\cdot{b_{2,1}} + \cdots + a_{m,n}\cdot{b_{n,1}} & a_{m,1}\cdot{b_{1,2}} + a_{m,2}\cdot{b_{2,2}} + \cdots + a_{m,n}\cdot{b_{n,2}} & \cdots & a_{m,1}\cdot{b_{1,p}} + a_{m,2}\cdot{b_{2,p}} + \cdots + a_{m,n}\cdot{b_{n,p}} \end{bmatrix}\)

  • Matrix Multiplication

Examples

Import matrix_product function from regressions library
>>> from regressions.matrices.multiplication import matrix_product
Multiply [[1, 2, 3], [4, 5, 6]] and [[2, 3], [5, 7], [11, 13]]
>>> matrix_2x2 = matrix_product([[1, 2, 3], [4, 5, 6]], [[2, 3], [5, 7], [11, 13]])
>>> print(matrix_2x2)
[[45.0, 56.0], [99.0, 125.0]]
Multiply [[1, 2, 3], [4, 5, 6]] and [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]
>>> matrix_2x4 = matrix_product([[1, 2, 3], [4, 5, 6]], [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
>>> print(matrix_2x4)
[[38.0, 44.0, 50.0, 56.0], [83.0, 98.0, 113.0, 128.0]]