What is scalar multiplication of matrices?

Question

4714 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-12-10T03:04:38

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.