Left Division vs Right Matrix Division – Matlab

There are two operators allowing to divide in Matlab:

• The right division represented by the symbol / (slash)
• The left division represented by the symbol \ (Backslash)

These two operators differ from each other

Using numbers, the right division will be the conventional division we all day make use of, so

Contrary to the right division, the left division reverse the division, meaning

Matrix division in Matlab

The right Matrix divide

Let’s consider two Matrices A and B

Using the right division

Matlab code

A=[1 2 ; 2 2];
B=[3 2 ; 1 1];
A/B % You can also use A*inv(B)

which returns

rewritten, it will look like this

The left Matrix divide

The right matrix divide is roughly the same as

Which leads to a complete different result from the preceding operator.

This technique can be used to quickly compute the solution of the equation

So, using our early defined matrices

will be written

A=[1 2 ; 2 2];
B=[3 2 ; 1 1];
A\B % You can also use inv(A)*B

which returns

Which rewritten will look like

The Matrix division, element by element

We thought it will be also necessary you have a grip on the element-by-element Matrix division in Matlab

To divide Matrices, element-by-element, the following formula is useful

Where

The code

A./B

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