Is matrixs multiplication random ?

[ManishR]

lets assume matrix A = [a]_mxn and B = _nxp

$$(AB)_{ij}=\sum_{r=1}^{n}A_{ir}B_{rj}$$

why is that ?

i guessed it would be

$$(AB)_{ij}=\sum_{r=1}^{n}A_{ir}B_{jr}$$ where m=p.

so is there any logic behind that or its just random ?

 

[LCKurtz]

No, it isn't random. Look at a simple 2 x 2 example:

y₁ = a₁₁x₁ + a₁₂x₂
y₂ = a₂₁x₁ + a₂₂x₂

Now let
z₁ = b₁₁y₁ + b₁₂y₂
z₂ = b₂₁y₁ + b₂₂xy₂

You can write these both in matrix form y = Ax and z = By

Now solve for the z values in terms of the x values to write z = Cx.

You will see that C = BA given by the usual matrix multiplication. That is why matrices are multiplied the way they are.

[Edit] Fixed typo.

 

[takahashi_s]

You mean C=BA, not AB.

 

[takahashi_s]

No, it isn't random. Look at a simple 2 x 2 example:

y₁ = a₁₁x₁ + a₁₂x₂
y₂ = a₂₁x₁ + a₂₂x₂

Now let
z₁ = b₁₁y₁ + b₁₂y₂
z₂ = b₂₁y₁ + b₂₂xy₂

You can write these both in matrix form y = Ax and z = By

Now solve for the z values in terms of the x values to write z = Cx.

You will see that C = AB given by the usual matrix multiplication. That is why matrices are multiplied the way they are.

You mean C=BA, not AB.

 

[LCKurtz]

You mean C=BA, not AB.

Yes, of course, thanks.