What is scalar multiplication of matrices?

1 Answer

Simply the multiplication of a scalar (generally a real number) by a matrix.

The multiplication of a matriz #M# of entries #m_(ij)# by a scalar #a# is defined as the matrix of entries #a m_(ij)# and is denoted #aM#.

Example:

Take the matrix

#A=((3,14),(-4,2))#

and the scalar #b=4#

Then, the product #bA# of the scalar #b# and the matrix #A# is the matrix

#bA=((12,56),(-16,8))#

This operation has very simple properties that are analogous to that of the real numbers.