By Kardi Teknomo, PhD .
LinearAlgebra

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When we multiply a real number Matrix scalar multiple with a matrix Matrix scalar multiple , we have the scalar multiple of Matrix scalar multiple . The scalar multiple matrix Matrix scalar multiple has the same size of the input matrix Matrix scalar multiple and it is obtained by multiplying each element of Matrix scalar multiple by Matrix scalar multiple that is Matrix scalar multiple .


Example
Matrix scalar multiple
Matrix scalar multiple


The interactive program below shows you the result of matrix scalar multiple. Your input is a matrix of any size but less than 100 scalar elements and a scalar number. Random Example will generate both random matrix and random scalar.

Matrix A = scalar k =

Properties

Some important properties of matrix scalar multiple are

  • Matrix scalar multiple is a commutative operation. When the order is reversed, you will still get the same result Matrix scalar multiple
  • Matrix scalar multiple is an associative operation. You can exchange the order of computation (operation inside parentheses are to be computed first) does not change the result Matrix scalar multiple .
  • Matrix scalar multiple is a distributive operation. You can distribute (and group) the scalar with respect to addition Matrix scalar multiple and multiplication Matrix scalar multiple .
  • Matrix scalar multiple is also an associative operation with respect to matrix product . You can exchange the order of computation (operation inside parentheses are to be computed first) does not change the result Matrix scalar multiple .
  • When the scalar is zero, matrix scalar multiple will produce a zero matrix Matrix scalar multiple
  • When the scalar is one, matrix scalar multiple will produce the input matrix itself Matrix scalar multiple
  • When the scalar is negative one, matrix scalar multiple will produce the negative of the input matrix Matrix scalar multiple

See also : matrix multiplication , matrix addition , matrix zero

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