- #1
zonde
Gold Member
- 2,961
- 224
To me it seems basic question or even obvious but as I am not mathematician I would rather like to check.
Is it true that these two matrices are both identity matrices: ##\begin{pmatrix}1&0\\0&1\end{pmatrix} ## and ##\begin{pmatrix}\frac{1}{\sqrt2}&-\frac{1}{\sqrt2}\\\frac{1}{\sqrt2}&\frac{1}{\sqrt2}\end{pmatrix}##? It's just that one of them would become diagonal with the right change of basis and the diagonal one would not be diagonal any more with that change of basis, right?
Is it true that these two matrices are both identity matrices: ##\begin{pmatrix}1&0\\0&1\end{pmatrix} ## and ##\begin{pmatrix}\frac{1}{\sqrt2}&-\frac{1}{\sqrt2}\\\frac{1}{\sqrt2}&\frac{1}{\sqrt2}\end{pmatrix}##? It's just that one of them would become diagonal with the right change of basis and the diagonal one would not be diagonal any more with that change of basis, right?