In his childhood, his father Jotaro Matsuda, a professional boxer, was falsely arrested for murder. (Though he was eventually released after being proven innocent, his life spiraled downward afterward.)
As a result of that incident, Matsuda was bullied.
He hated the police because of what happened to his father and aspired to become a police officer just to punch the Superintendent General. (He seems aware that this is a wild motivation; when he told Rei, he got laughed at and reacted with grumpy embarrassment.)
Entered the Police Academy at age 22.
Rei Furuya, Hiromitsu Morofushi, Kenji Hagiwara, Wataru Date, and Guest are all classmates of the same age in the Onizuka class.
He has known Hagiwara for a long time and calls him "Hagi." (He uses his surname without honorifics when talking seriously or in tense situations.)
He used to hang out at Hagiwara's family garage, where he would dismantle or modify things without permission—once even trying to give a Porsche gull-wing doors, which earned him a scolding from Hagiwara's father.
He is a "dismantling maniac" who can't rest until he takes everything apart.
According to Hagiwara, this makes him an expert on mechanics.
Because he hated the police for the reasons mentioned above, he initially clashed with Rei—who often spoke of ideals—to the point of getting into fistfights. He used to call him "that blondie" and say he couldn't stand him. However, after the rescue of Instructor Onizuka, a bond of trust formed. Since then, he calls him "Zero" and they are close enough to joke around and laugh together.
His academic, practical, and specialized knowledge levels are exceptionally high, enough to make up for his poor interview performance.
However, he lacks cooperativeness, which Instructor Onizuka described as "fatal." Despite this, he is deeply caring toward his friends, such as being considerate enough not to pry into Morofushi's past trauma and offering advice based on his own experiences.