I found this schematic online for an audio amplifier and I noticed the 100k was some sort of feedback system between the base of the first stage and the emitter of the next. How would you describe this feedback mechanism? What is its effect on the gain and bandwidth of the system?
Both transistors have local negative feedback - provided by the emitter resistors. This feedback mechanism is effective for both dc (operational point) and for ac (signals).
The 100k resistor fulfills two tasks: (a) It determines the bias point of the first transistor (together with the 10k resistor at the base) and - at the same time - it provides overall negative feedback for additional stabilization of the DC quiescent operational point of the whole circuit. This feedback path is NOT effective for signals due to the 10uF capacitor to ground. Therefore, THIS feedback path has practically no influence on gain and bandwidth (in contrast to to the feedback provided by the emitter resistors.
Comment: The last sentence is correct as long as the signal input has a very small source resistance. Otherweise the 100k path allows a very small signal feedback also.