- Thread starter
- Moderator
- #1

- Jan 26, 2012

- 995

-----

**Problem**: Let $A$ and $B$ be $n\times n$ matrices with real entries. Show that $\langle A\mathbf{u},B\mathbf{v}\rangle = \langle \mathbf{u}, A^TB\mathbf{v}\rangle$ for any vectors $\mathbf{v},\mathbf{w}\in\mathbb{R}^n$, where $\langle\cdot,\cdot\rangle$ denotes the standard inner product on $\mathbb{R}^n$.

-----

Remember to read the POTW submission guidelines to find out how to submit your answers!