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This paper presents a solid foundation for implementing analog vector-matrix multipliers (VMMs) in field-programmable analog arrays (FPAAs). Custom analog VMMs have been demonstrated to be 1000 times more power efficient than commercial digital implementations. However, no previous analog VMM discussion has carefully provided all of the implementation and performance considerations needed to utilize such a system. We utilize the FPAA because it provides an ideal platform for embedding low-power analog processing into larger systems. FPAAs allow the analog processing system to be rapidly prototyped, implemented at low cost, and easily reconfigured in the field. This paper can double as a complete analog VMM design specification, as well as a systematic tutorial on developing general systems with FPAA hardware. We detail the aspects of VMM topology choice, completely analyze the performance metrics, and describe the methods and tools involved in FPAA synthesis.