Does the statement: $$v^TA=v^T$$ Imply $$Av = v$$
Where A is an nxn matrix and v a vector.
Asked
Active
Viewed 108 times
0
-
2No. It's equivalent to $A^\top v=v$ – b00n heT Nov 10 '19 at 19:36
-
I transposed the first equation, not the second – b00n heT Nov 10 '19 at 19:38
-
For an example, let $A=\begin{pmatrix}1&0\1&0\end{pmatrix}$ and $v=\begin{pmatrix}1\0\end{pmatrix}$. Then $v^TA=v^T$, but $Av = \begin{pmatrix}1\1\end{pmatrix}$. – Math1000 Nov 10 '19 at 19:41
-
@b00nheT I realized my error, and hence deleted my first comment. – Math1000 Nov 10 '19 at 19:41
-
The transpose of a product is the product of the transposes in reverse order – J. W. Tanner Nov 10 '19 at 19:44
-
Surely that example doesn't apply as $Av =/= v$ in this case. – PolynomialC Nov 10 '19 at 19:44