The Time Trapper created a pocket universe with its own Earth as part of a plan to manipulate the Legion of Super-Heroes. After Superboy went into the future to save the world, Lex Luthor, a noble scientist, created a lifeform from protomatter with Lana Lang's genetic material to aid them in the war against three rogue Kryptonians, General Zod, Zaora and Quex-Ul.
Matrix was created by Karl Kesel and John Byrne.
Modern Age / Pocket Universe
The Matrix's first appearance is in Superman #16. The Matrix's first meets Superman in Superman #21. Matrix left her dead world and travel to Superman's Earth. Matrix took on a feminine form and paid homage to her savior by using her powers to become Supergirl of this world.
Matrix would meet Lex Luthor jr. (the son of Lex, who really the real Lex in a young clone body of his), she became his bodyguard/love interest.
Major Story Arcs
Modern Age / Pocket Universe:
The shape changing Matrix sent from her world to a parallel world, hoping Superman would help. He answered the call and came back to her world. Superman forced to kill the three Kryptonians to save their world, but it was to late. Superman could only save Matrix, who reduced to an amorphous mass after the fight. Superman brought Matrix to his world to recover on the Kent Farm. While live with the Kents'.
Matrix believe she was Superman and took on his form. She later fought the real Superman which force Matrix come back to her senses. But Matrix, feared of losing control again and hurting the Kents. She left Earth and went into outer space, she would later come back to Earth during Panic In The Sky event. The naivety Matrix fell under Lex Luthor's influence for a while, until she saw the manipulative criminal he is. She also had a brief stint in the Teen Titans.
Matrix saved the life of Linda Danvers, by merging their life essences. A new being was created with new abilities such as increased strength but reduced shape changing.
In time she discovered the violent life Linda had led and sought to redeem her. During her encounters with various supernatural entities, she discovered she was a reborn Earth-Angel. One of three on Earth.
She also lost her shape-shifting abilities as she began to see herself as just Linda or Supergirl. The part of her protoplasmic form that didn't merge became an insane creature and fought Linda/Matrix until she was absorbed by the Angel of Light, Blithe.
Matrix and Linda were eventually separated by Demon Queen Lilith. Matrix was guarded by a woman called Twilight. When Linda rescued Matrix after fighting and then gaining Twilight as an ally, Twilight was fatally injured by Lilith. Linda convinced Matrix to bond with Twilight to heal her. Twilight/Matrix used her healing powers to restore Linda to her previous power levels. Twilight and Matrix whereabouts are unknown at this time.
No More Matrix
Matrix/Linda Danvers was believed to have been retconned out of existence due to Superboy-Prime punching the walls of reality. However, Geoff Johns stated that Linda Danvers still exists, and that she would make her return to the DCU in July of 2008. Linda, not Matrix, had appeared in Reign in Hell, still being considered part angel despite having Matrix leave her before. She has been referenced as Supergirl in the mini-series, thus implying that her series remains in continuity. As far as Matrix is concerned there has been no mention of her and her existence in DC remains uncertain.
Supergirl appears in the two issue mini-series Supergirl Convergence: Supergirl (Matrix), as part of the mega DC crossover that will take place in several timelines. The series will also feature Lady Quark and Ambush Bug. The writer of this mini-series has stated that this is a farewell for the character, her last story.
Matrix appears as an angel who trying to help Linda Danvers.
Powers & Abilities
Matrix's powers are:
Matrix uses psychic abilities to emulate the powers of a Kryptonian. It allows her to have Super strength, speed, and endurance. It allows her to possess flight and makes her invulnerable against most conventional attacks.
Along with her Psychokinesis Matrix has the ability to affect space and matter around her. She can create force fields of psychic energy or she can turn it on the offensive and use psychic blasts against her enemies.
Matrix possesses the ability to render herself invisible by deflecting light waves and sound waves with her aura, she could cloak herself (becoming become invisible and inaudible, even to Superman's hearing)
She could morph into a humanoid form of similar mass, and use her psi-power to rearrange the molecular structure of fabrics, and alter clothing and costumes with her thoughts (an ability that enabled her to change her clothing when she changed shape, and turn tattered rags into a costume for Superman).
After combining herself with Linda Danvers and becoming one of the three Earth Angels, the Earth Angel of Fire, in her case, Matrix lost her invisibility and shape-shifting, but soon learned that she had new powers to compensate for the loss. Her flame abilities most notably manifest as fiery wings and flaming eye beams (similar but to Superman's heat vision, but different in that they are actual flames, and, of course, angelic in origin, rather than being biased on biology apparently).