Software Defined Radio (SDR) is an advanced wireless transmission paradigm that permits to support all the consumer wireless protocols such as 2G, 3G, LTE, Wi-Fi (2.4 GHz and 5GHz), Bluetooth and Zigbee, by software rather than hardware. A typical frequency band of operation is in the range 0.5-6 GHz. The challenge to bring a SDR system on portable devices is the availability of Ultra-wide band compact amplifiers with high gain over a wide frequency band. A novel hybrid Silicon BJT and E-pHEMT matrix amplifier with two rows and four columns (2 by 4) of transistors is designed realized and tested demonstrating 0.65-5.8 GHz frequency band to satisfy the SDR specifications. The novel optimum filter matching technique is applied to optimize the performance and overcome the limit of the hybrid approach. The proposed matrix amplifier exhibits an average gain of 37.5dB and average output power of 18dBm across 0.65GHz-5.8GHz band with only 3V supply voltage. The gain is the highest in the state of the art for the frequency range. A bandwidth of 5.15 GHz, 20.3dBm one dB compression point at 1.35GHz, 10% to 16% power added efficiency and 1.2W DC power consumptions are obtained.