Matrix division

[zooropa1844]

Good morning,

I saw in a different forum a screen capture showing a division of two matrices done with a Prime. Does anybody know what exactly the Prime does when you ask it to divide two matrices? Because it doesn't seem to be the elementwise division nor the division of matrices is a well-defined operation between matrices.

Regards

[Arno K]

It does implicitely what you would do when you had to do it by hand, A/B is performed as A*B^-1.
Arno

[zooropa1844]

It seems wrong to me that HP promote the idea among students that "matrix division" is an acceptable matrix operation. The TI Nspire CAS wisely doesn't allow it.

Regards

[Werner]

(04-09-2018 09:23 AM)Arno K Wrote:  A/B is performed as A*B^-1.
Arno

I would hope not. I hope it returns B^-1*A, and calculates it as solve (B*X = A), not explicitly calculating the inverse.
That's what all the other HP-calcs (42,48,49,50) do.

Cheers, Werner

[Arno K]

Hm, wrong, may be, but if the division is not possible as the second matrix is not invertable you are told that and as usual one has to know what one does when a tool like that calculator is used.
Arno

[zooropa1844]

I could check that it does what Werner told and before doing it, it displays a message saying A/B is a misleading notation and that it's going to compute inv(B)*A.

Regards

[Arno K]

I did not even check that, clear is that it multiplies by B^-1, but you have to be careful (solve X*B=A instead of B*X=A), so I always use the multiplication above in appropriate form. On the mentioned other HP-calcs I used that division as a shortcut when I solved A*X=b, b being a vector, there it did not matter.
Arno