I was recently trying to understand wireless channel estimation. So supposedly at the reciever we have to pass the signal through, an inverse channel filter to

I was recently trying to understand wireless channel estimation. So supposedly at the reciever we have to pass the signal through, an inverse channel filter to recover the transmitted signal. A friend of mine asked: what if the channel has no inverse? I had no idea how to respond to this because of my poor intuitive understanding of linear algebra. 3blue1brown's video series explained this beautifully as, when the inverse doesn't exist, the transformation packs the input into a lower dimensional space. So in communication terms the transmitted signal is completely lost anyway. So we should look for a better channel to communicate. Now needless to say there is a lot I am probably wrong about, but I'm still very grateful for that excellent video series.