Matthew gave the form of a guilty plea to all three charges in the Fairfax case: attempted capital murder, abduction and sexual assault.
The plea means the jury will play no role in deciding Matthew's sentence, it will be done solely by Judge David Schell. Sentencing is scheduled for October 2.
Prosecutor Ray Morrogh said he was not yet ready to say what kind of sentence he will seek. Matthew had no deal with prosecutors, Morrogh said.
His plea came after the prosecution rested its case with DNA evidence found under the fingernail of the woman who said she was assaulted in the Fairfax case.
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In the key testimony, forensic scientist Elizabeth Ballard said the chance of a person other than Matthew being the source of the fingernail DNA was less than one in 7.2 billion.
Defence lawyers tried unsuccessfully to get the judge to strike the case, saying the DNA evidence was insufficient for a conviction and that the victim's description did not exactly match the way Matthew looked at the time.
"He physically picked her up like a baby ... And carried her into the darkness," Morrogh said. "He did that to render her helpless for his purpose: to kill her and molest her for his pleasure."
Matthew's family declined to comment as they left the courtroom.
The victim, who flew back from India to testify, told jurors on Monday that her attacker grabbed her just steps from the door to her townhouse and carried her into a darkened area, where he ripped off her clothes and molested her.
The woman did not explicitly identify Matthew as her attacker during her testimony. She will speak again at a hearing June 18, giving impact testimony ahead of Matthew's sentencing.
The Associated Press generally does not identify alleged victims of sexual assault.