I am surprised if the Toyota compressor is not compatible as the engine installation is pretty much the same, here at the middle of the end of the world we often have to adapt bits from something else as parts are simply not available,
My GTM kit car build is intended to have a BL Mini as a donor car for parts, there are no Mini's here, so my Mini hubs are fitted 1.6 Carolla front discs and callipers on all 4 corners,
I wanted to fit an ac as we can have 45c temperatures, Mini's were never factory fitted with ac, I'm not sure what my compressor is off, but it is compact and just squeezes in above the alternator with an adapted pully and its own drive belt.
John
GM used their own systems for the heating and cooling, along with the radio. Toyota used their systems for cooling and heating, along with their radio. None of these parts interchange. The A/C compressors have different size pulleys on them and that is why the drive belts are different on the Vibe vs the Matrix too. This is also why the Vibe has the clicking broken outside air duct plastic gear issue and the Matrix does not have that problem. They are completely different systems in the Vibe, and in the Matrix. So the short answer is no, the compressors will not interchange.
I'm lucky enough to have access to a workshop and can make/adapt things to fit, the ac compressor has 2 pipe connections, usually JIC thread and normally a single electrical connection to engage the clutch to regulate the temp setting, making/adapting the drive pully to the size you need is not a big problem if Matrix and Vibe are different, I can't check as I don't have access to a Matrix, but would be most surprised if the mounting bracket fixing holes on the engine block are different.
Having fitted an ac where they have not been fitted before, I can only say nothing impossible if you want or need to do it.
John