- #1

victorvmotti

- 155

- 6

##\mathcal{H1} \otimes\mathcal{H2}={T}\big/{\sim}##

The definition for the

**equivalence relation**is given in the lecture vidoe as

##(\sum_{j=1}^{J}c_j\psi_j, \sum_{k=1}^{K}d_k\varphi_k) \sim \sum_{j=1}^J\sum_{k=1}^Kc_jd_k(\psi_j,\varphi_k)##

But is this correct?

A linear combination of pairs on the right hand side is equivalent to

**only one pair**on the left hand side.

Shouldn't we define the equivalence relation as below so that we have on

**both sides linear combination of pairs**?

##\sum_{i=1}^Ia_i(\sum_{j=1}^{J}c_j\psi_j, \sum_{k=1}^{K}d_k\varphi_k) \sim \sum_{i=1}^I\sum_{j=1}^J\sum_{k=1}^Ka_ic_jd_k(\psi_j,\varphi_k)##