Explain why the notation A/B is ambiguous when A and B are matrices,even if det B isnot equal to 0.

Printable View

- Sep 8th 2009, 12:33 AMroshanheroMatrix
Explain why the notation A/B is ambiguous when A and B are matrices,even if det B isnot equal to 0.

- Sep 8th 2009, 12:48 AMBobP
It's not ambiguous, the operation of dividing one matrix by another is not defined.

- Sep 8th 2009, 04:36 AMHallsofIvy
I disagree with BobP. "Dividing", in any group, field, or ring, means multiplying by the inverse and

**is**defined in a vector field.

The "ambiguity" is in A/B, and the reason "multiplying by the inverse" is never written that way, is that multiplication of matrices is not commutative. That could mean either $\displaystyle AB^{-1}$ or $\displaystyle B^{-1}A$.