Multiplication with Vectors

scalar_product_vector(vector, scalar)

Calculates the product of a vector and a scalar

Parameters

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

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

Raises

  • TypeError – First argument must be a 1-dimensional list

  • TypeError – Elements of first argument must be integers or floats

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

Returns

product – List of numbers in which each element is the product of the scalar factor and the corresponding element from the input vector

Return type

list of int or float

See also

scalar_product_matrix(), vector_sum()

Notes

  • Vector: \(\mathbf{a} = \langle a_1, a_2, \cdots, a_n \rangle\)

  • Scalar: \(c\)

  • Scalar product: \(c\cdot{\mathbf{a}} = \langle c\cdot{a_1}, c\cdot{a_2}, \cdots, c\cdot{a_n} \rangle\)

  • Scalar Multiplication

Examples

Import scalar_product_vector function from regressions library
>>> from regressions.vectors.multiplication import scalar_product_vector
Multiply [1, 2, 3] and -2
>>> product_3d = scalar_product_vector([1, 2, 3], -2)
>>> print(product_3d)
[-2, -4, -6]
Multiply [-5, 12] and 3
>>> product_2d = scalar_product_vector([-5, 12], 3)
>>> print(product_2d)
[-15, 36]
dot_product(vector_one, vector_two)

Calculates the product of two vectors

Parameters

  • vector_one (list of int or float) – List of numbers representing a vector

  • vector_two (list of int or float) – List of numbers representing a vector

Raises

  • TypeError – Arguments must be 1-dimensional lists

  • TypeError – Elements of arguments must be integers or floats

  • ValueError – Both arguments must contain the same number of elements

Returns

product – Number created by summing the products of the corresponding terms from each input vector

Return type

float

See also

matrix_product()

Notes

  • First vector: \(\mathbf{a} = \langle a_1, a_2, \cdots, a_n \rangle\)

  • Second vector: \(\mathbf{b} = \langle b_1, b_2, \cdots, b_n \rangle\):

  • Dot product of vectors: \(\mathbf{a}\cdot{\mathbf{b}} = a_1\cdot{b_1} + a_2\cdot{b_2} + \cdots + a_n\cdot{b_n}\)

  • Dot Product

Examples

Import dot_product function from regressions library
>>> from regressions.vectors.multiplication import dot_product
Multiply [1, 2, 3] and [4, 5, 6]
>>> product_3d = dot_product([1, 2, 3], [4, 5, 6])
>>> print(product_3d)
32.0
Multiply [-5, 12] and [3, -7]
>>> product_2d = dot_product([-5, 12], [3, -7])
>>> print(product_2d)
-99.0