Following post was made in response to a question in New User Forum. Of course the OP was not really interested in my answer, so I moved the discussion here.
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I have used an HDMI matrix switcher in the past with good results. Monoprice HDX 404E. I never noticed any restrictions or protocol issues.
But I recently did a bit of remodeling and have re-wired not to use it. I found that it was almost never set to what I needed at the time. And on movie nights, or when I was tired, it was a hassle trying to remember the row and columns - "let's see, the projector is B3 or is it C6"?
If you don't already have your a/v receiver, put your money into getting the most versatile one you can afford: multiple HDMI outputs (for TV and projector) and multiple inputs of every kind, with "up-conversion".
Such a device will allow you to plug in anything and they will be converted to the required HDMI output for your HD TV and projectors. The most advanced a/v equipment will even allow multiple zones that can play different sources at the same time - giving the equivalent of a matrix switch.
Since I already had a bunch of stuff, not starting from scratch, I tried the matrix switch and it worked very well. But over time, I found using it was too confusing. So I have found a way to rewire and do without it, and will just live without a couple of connection possibilities that I didn't use much anyway.
Oh, another important thing: my re-wired system was partly enabled by my discovery of features of my projector that I was not using.
I have an Epson 3D projector with multiple inputs and a wireless connection.
The big discovery for me was that the wireless transmitter had 5 (!) HDMI inputs, and also a hard-wired HDMI output to drive the TV. It also has an optical output that connects to the a/v receiver. So, half of my sources connect to the TV, projector and receiver thru the wireless transmitter switch, and the other half connect directly to the receiver - which can drive both the projector and TV also. The final connection is that I use an optical output from my TV to the a/v receiver, so that the TV smart apps can play thru my audio system.
I am working on a diagram, if it is of any interest to you.