- #1
Bipolarity
- 776
- 2
Suppose A and B are matrices of the same size, and x is a column vector such that the matrix products Ax and Bx are defined.
Suppose that Ax=Bx for all x. Then is it true that A=B?
I know that this is true and I can prove it using the idea of transformation matrices, and viewing Ax and Bx each as linear transformations and showing that those two transformations are equivalent, but I was curious if this can be proved without appealing to the notion of a linear transformation.
Tips?
BiP
Suppose that Ax=Bx for all x. Then is it true that A=B?
I know that this is true and I can prove it using the idea of transformation matrices, and viewing Ax and Bx each as linear transformations and showing that those two transformations are equivalent, but I was curious if this can be proved without appealing to the notion of a linear transformation.
Tips?
BiP