0
votes
0answers
95 views

Operator Adjoints and Non-Symmetric Inner Products

Let $V$ be a finite dimensional vector space (over $C$ if that makes a difference), and let $T$ be a linear operator on $V$. Now if $(\cdot,\cdot)$ is an inner product on $V$, then it is well-known ...
5
votes
2answers
401 views

Can finitely many hermitian (positive-semidefinite) operators always be embedded into a small dimensional space preserving inner product?

Given $n$ hermitian (positive-semidefinite) operators $Q_1,\cdots,Q_n$ in finite dimensional Hilbert space (the dimension can be very large), is there a mapping $\phi$ maps $Q_i$ to $P_i$, which ...