People are buying large quantities of very expensive GPUs just to do some matrix manipulations, so why not FPGAs?

But the point is that you don't have that much FPGA-specific code - once someone does the matrix manipulations and the proper integration, everyone else can just run e.g. tensorflow code on it faster and/or cheaper without specific expertise; if a FPGA vendor can do this one-time investment in software tools, then they can compete for a slice of the large pie of hardware revenue that nvidia now has for itself.

But, assuming that "matrix manipulation" code has existed for FPGAs for a while, since verilog and VHDL are quite old, the question remains: why hasn't (a) an FPGA vendor already done this and already actively selling a tensorflow solution or (b) NVidia pursuing this? I have a feeling there are more factors at work than just whether or not it's possible.

It's a very expensive, very customizable appliance. Hence Amazon's AWS F1 instance and Nimbix cloud.