Combat Pragmatist: In keeping with both his characterization from the novel (as well as historically) Musashi occasionally eschews fighting purely honorably in favor of using what simply works. For example, he begins his fight against the seventy Yoshioka swordsmen by incapacitating/killing them with unarmed blows before attacking with weapons he has taken from his opponents, and attacking from the shallowest direction (that is, that with the fewest swordsmen between him and his target)... and he doesn't hesitate to resort to the Groin Attack either!
Oedipus Complex: He had a complicated relationship with his father, Shinmen Munisai, to say the least. Takezo tried to kill him several times as a child, and as a young man he became obsessed with surpassing him.
One-Man Army: Musashi cuts down about seventy highly trained and nationally respected Yoshioka swordsmen — that is, the entire school membership, after diving right into their center at the start of the conflict and mortally wounding their leader. This single-handedly catapults him to a national figure and doubles as a Crowning Moment of Awesome.
To Be a Master: Deconstructed. His driving motivation is to become "unrivaled under the sun", but the closer he gets to achieving this goal the more realizes how little the title means, especially when his massacre of the Yoshioka school ends with him crippled and forced to crawl away past their already-rotting corpses.
Dirty Coward: And it fuels his inferiority complex to Takezo.
Foil: To Musashi naturally. They both start out at the same place. Musashi pursues martial perfection, often living like an ascetic and choosing to live in privation even when better options are available. On the other hand, Matahachi ends up wallowing in worldly pleasures, taking every advantage of every opportunity to make himself more comfortable.
Glory Seeker: Leaves Miyamoto village and go to fight in the battle of Sekigahara to make a name for himself. He fails pretty badly.
Miles Gloriosus: He borrows Kojiro's identity for a while to live of his reputation.
An orphan raised at the temple in Miyamoto village, Otsu is a childhood friend to both Musashi (Takezo at the time) and Matahachi. She was originally betrothed to Matahachi, but then he broke it off after he decided to run away with Oko and not return to Miyamoto village. She instead fixates on Takezo/Musashi (it's implied that he was actually the one she was in love with all along) and leaves Miyamoto to go after him when he heads out to make his name as a swordsman.
Adaptational Badass: Otsu in the original novel was pathetic and needy, with a very weak constitution, often to the point of getting physically ill over emotional matters. In the manga, she is much more self-sufficient and even takes lessons in self-defense from the Yagyu.
Moses in the Bullrushes: Kojiro is introduced in this fashion. His father had him sent by boat from a besieged castle to be raised by his master, Kanemaki Jisai. His mother had been swept overboard and killed during the voyage and he would have suffered the same fate if Jisai hadn't saved him.
The second genration master of the Yoshioka Kempo's school of swordfighting in Kyoto. While a superbly talented swordsman, he is also hedonistic and carefree, though he can and will be serious and take appropriate measures in times of crisis.
Adaptational Badass: In the novel, he really is little more than a hedonistic pretty boy, who is actually inferior to Denshichiro in swordsmanship.
Big Brother Instinct: While he remains an Aloof Big Brother, he still ultimately cares for Denshichiro. He even tries to kill Musashi in a sneak attack to prevent him from fighting Denshichiro, having already known that Musashi would win... unfortunately for Seijuro, Musashi had surpassed him too.
Can't Catch Up: As hard as he works he can never match Seijuro in swordsmanship. And in the year leading up to their rematch he utterly fails to keep up with Musashi, who makes the most of the year and grows into one of the very best swordsmen in the land.
Honor Before Reason: He insists on fighting his rematch with Musashi even though he is clearly outmatched and stands nothing to win.
He also expels Ueda Ryohei, his de facto brother, for trying to protect him by arranging for Musashi's demisenote although his will reveals that after his death, Ryohei was to be readmitted and succeed him as headmaster.
Over Shadowed By Awesome: Skilled and dedicated swordsman, but hopelessly outranked by his brother and eventually Musashi.
Sibling Yin-Yang: Very much so. Seijuro is a carefree pretty boy blessed with supreme talent and confidence, and Denshichiro is a stern, hulk of a man, who works hard trying to be as good as his brother.
A senior disciple of the Yoshioka School. He was raised by the Yoshiokas and is almost regarded as a brother to Seijuro and Denshichiro.