division of two vectors

What is the result of A/B ???? (if A and B are same 3x1 row vectors) Example:

A=[-1;1;7]
B=[5;7;-2]
A/B

in Matlab gives: ans =

         0   -0.1429         0
         0    0.1429         0
         0    1.0000         0

[Adam]

You seem to have answered your own question by giving us the result.

doc mrdivide

will answer the question more generally though.

If you want element-wise division then use

A./B

[mimalo salina]

I know that mrdivide means the matrix right division, but here in my case i have two vectors and A./B is the division element by element, my question is what does mean A/B ?

[Adam]

It means what it says on the help page! If you know it means matrix right division then what is your question? A/B means matrix right division, that is the answer!

[mimalo salina]

yes, but A ,B are same 3x1 row vectors, it seems false, because , we can't divide two vectors? i want to undersand the meaning of this result !

[Guillaume]

"we can't divide two vectors". Well, obviously you can apply the / operators to two vectors since matlab give you a result.

As Adam said in his comment and as Jan showed in its answer, what it does is fully documented. It solves a system of linear equation. If the right-hand side is not a square matrix as is the case here, it is solved using least-square method. As documented:

If A is a rectangular m-by-n matrix with m ~= n, and B is a matrix with n columns, then x = B/A returns a least-squares solution of the system of equations x*A = B

I'm not sure what other answer you are looking for.

Answer 1

[Jan]

C = A / B determines the matrix C such that:

C * B = A

Try it:

A = [-1;1;7];
B = [5;7;-2];
C = A / B;
C * B

>> [-1; 1; 7]

Answer 2

[John D'Errico]

A=[-1;1;7];
B=[5;7;-2];

First of all, A and B are NOT row vectors. They are column vectors. Thus, A is a vector in column orientation.

A
A =
  -1
   1
   7

Next, what is C=A/B?

C = A/B
C =
                       0        -0.142857142857143                         0
                       0         0.142857142857143                         0
                       0                         1                         0

It is a matrix, such that if possible, we will have A=C*B.

C*B
ans =
  -1
   1
   7

In some cases of vectors or matrices of varying sizes, that will not be possible.

Answer 3

[mimalo salina]

Action closed.

Thanks a lot for all your answers!

Kind regards.