Sōichirō Kiryūin

Sōichirō Kiryūin, also known by his alias Isshin Matoi, was the husband of Ragyō Kiryūin and father of Ryūko Matoi and Satsuki Kiryūin. He was a brilliant scientist and Life Fiber researcher who went on to create Senketsu, the Scissor Blades, and Nudist Beach. He was murdered by Nui Harime under Ragyō's orders, impaled by his own Scissor Blade.

After the presumed death of his daughter, Sōichirō faked his death along with his daughter and forged a new identity, calling himself "Isshin Matoi" and raising the infant Ryūko on his own in a mansion.

Sōichirō had aimed to "thwart the ambitions of the Kiryūins by using the Kamui". His actions are the posthumous driving forces behind the plot of the series—including Ryūko's search for her father's killer.

As Sōichirō Kiryūin
As Sōichirō, he was a youthful man with a medium-length mullet that has large bangs covering the right side of his face.

As Isshin Matoi
When he took on the guise of Isshin, his appearance became that of an old man with a long beard, a hunched back, an eye patch over his right eye and he was often seen with a small mouse on his shoulder.

Early Life
Sōichirō Kiryūin married Ragyō Kiryūin and worked alongside her in the research of Life Fibers. A year after the birth of their first child, Satsuki Kiryūin, Ragyō attempted to merge the child's body with Life Fibers. This failed - Satsuki was too old to be compatible with them. This caused Ragyō to resolve to using her second child, whom she was at the time pregnant with, as her next test subject. After the birth of their second child, Ragyō used her unnamed daughter as another test subject. However, the baby supposedly died during the experiment. After the baby's "death", she disposed of her for her apparent incompatibility. Unbeknownst to Ragyō, Sōichirō had faked their daughter's death and plotted to turn against his wife and to destroy all Life Fibers.

For the next five years, Sōichirō secretly raised the baby whose death he faked in an mansion, naming the girl Ryūko Matoi, while raising his oldest daughter in a separate home. Since he knew he would soon be punished for his betrayal and assassinated by Takiji Kuroido, he taught Satsuki, who at the time was five years old, about the secrets behind Life Fibers, its research and her presumed deceased sister, leaving her with the legacy of the rebellion against the Life Fibers. Sōichirō went into hiding after an assassination attempt by Takiji; faking his death, he forged a new identity as Isshin Matoi, altering his appearance to that of a short, hunchbacked old man. At some point, he worked closely with Aikurō Mikisugi, Tsumugu Kinagase and Kinue Kinagase where one of their experiments lead to Kinue's death.

Death
Six months before the events of the main story, Isshin was attacked by Nui Harime, who was sent to his laboratory to retrieve his creation under Ragyō's orders. As Nui approached the building, Isshin hid Senketsu. He then fought against her until he was driven back and forced to use the Rending Scissor, a pair of scissors that can cut and prevent Life Fibers from regenerating. Isshin was eventually overwhelmed and mortally wounded by the scissors when Nui managed to snag them from his hands. In a moment of distraction upon hearing Ryūko's voice, Nui ended up having her left eye taken by Isshin, who split the scissors in two. In a fit of rage, she took the scissor half used to damage her eye and slashed Isshin three times before thrusting the blade into his stomach and fleeing.

Ryūko found Isshin slumped on the ground with the other scissor half-driven through his body. He told her that, if she wanted to have a peaceful life, she was to leave him there and walk away. If she wished to fight in his place, however, she should take the very Scissor Blade that was used to kill him. Isshin proclaimed to Ryūko that she would be sure to find his assailant, but a cruel fate would be in store for her. Before he could say anything else, Ryūko saw Nui wielding the Scissor Blade, but couldn't make out the silhouette. With the other half of the scissor in her hands, she immediately gave chase, ignoring the pleas of her father, who said he still had much to say. The mansion then exploded with Isshin still inside.

At some point before his death, Isshin sent a letter to Aikurō asking him to lead Ryūko to Senketsu.

Ryūko Matoi
According to Ryūko herself, the two never had a close relationship. Isshin spent a great part of his time with his research, leaving him little time to spend with his daughter. Coupled with the lack of a mother, this led Ryūko to lead a lonely life, eventually becoming a juvenile delinquent. However, while little is known about Isshin's actual personality, he obviously loved his daughter deeply enough to risk his life by betraying Ragyō and REVOCS and sending a letter to Aikurō requesting him to aid Ryūko.

Satsuki Kiryūin
As her father, Sōichirō trusted Satsuki with the true nature of the Life Fibers prior to his disappearance and subsequent faked death. A memory of Sōichirō proclaiming Junketsu to be her 'wedding dress' and the forboding consequences stick with her as she tries to conquer it. She proclaims to Ragyō that she is fighting to avenge him and her baby sister. His identity as "Isshin Matoi" remained unbeknownst to Satsuki until late in the war against Ragyō.

Ragyō Kiryūin
While Sōichirō obviously loved Ragyō at the time they got married, that love disappeared completely by the time Ragyō used her own daughters as test subjects to observe their resistance to Life Fibers. Sōichirō eventually left his wife and dedicated his life to counteracting her goals.

Senketsu
As Senketsu's creator, Isshin left a bit of his likeness for Ryūko. Senketsu, in his normal state, shares an eyepatch and "mustache" (part of the scarf) with Dr. Matoi. Senketsu only knows what his creator looked like. However, after Ragyō's defeat in Episode 24, he tells Ryūko that he is sure that her father is satisfied.

Trivia

 * The name Sōichirō means "general, whole, all, full, total" (総) (sō), "one" (一) (ichi) and "son" (郎) (rō).
 * The alias name Isshin means "one person, oneself" (一身).
 * Sōichirō's surname Kiryūin means "demon, ogre" (鬼) (ki), "dragon" (龍) (ryū) and "hospital" (院) (in).
 * The alias surname Matoi means "wear, wrap, tie, follow around, collect" (纏).