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Active-matrix is the tech commonly found in LCD displays, most notably computer monitors and TVs.
It gets its name from using a matrix of TFTs and capacitors to control the brightness of the displayed image.
Additionally, the tech modifies the RGB of each individual pixel via its capacitors.
The TFT matrix gets the term "active matrix" because the capacitors are always active when the monitor is in use, working on brightness and colors.
Active-Matrix displays are significantly faster than their passive-matrix brethren and kills the effect of "ghosting."