what does A/b mean when solving matrix Ax=b

A/b

Answer 1

[Steven Lord]

The \ operator (mldivide function) solves for x in A*x = b.

The / operator (mrdivide function) solves for x in x*A = b.

Answer 2

[Voss]

https://www.mathworks.com/help/matlab/ref/mldivide.html

Answer 3

[Walter Roberson]

If you have A*x = b then x = A\b is very likely what you need

But if for some reason you want to know what meaning A/b would have in that situation, then:

If A*x = b then A*x*pinv(x) ~~ b*pinv(x) . But A*x*pinv(x) ~~ A because x*pinv(x) ~~ identity matrix. So A*x*pinv(x) ~~ b*pinv(x) ==> A ~~ b*pinv(x) .

Now right-mutiply both sides by pinv(b) to get A*pinv(b) ~~ b*pinv(x)*pinv(b)

Now A*pinv(b) is expressible in MATLAB as A/b, so A/b ~~ b*pinv(x)*pinv(b)

Unfortunately for unknown x that does not get you anywhere useful... except that there are some restricted cases in which pinv(x)*pinv(b) == pinv(b)*pinv(x) and if you just happened to fall into one of those then A/b ~~ pinv(x)

But in practice there is seldom a useful relationship between A/b and A\b. Most of the time you cannot even do both operations due to the restrictions on the column dimensions that \ and / have.

There are however relationships between the operators. According to the Tips,

The operators / and \ are related to each other by the equation B/A = (A'\B')'