The shooter's name is Cho Seung-Hui, a 23-year-old, who was a senior and an English major at the school, police said. Cho maintained a residence in Centreville, Va., but also lived in a campus dormitory, police said.
Receipts found in the gunman's backpack allowed authorities to trace one of the two handguns used in the shootings, though the serial numbers for both weapons were wiped clean, CBS News reports. Cho carried a 9 mm handgun and a 22 mm handgun during the shootings, police said.
Cho killed at least 30 people locked in a classroom.
Ballistics tests found that one of the guns used in that attack was also used in a shooting two hours earlier at a dorm that left two people dead, Virginia State Police said.
Cho committed suicide after the attacks, and there was no indication Tuesday of any possible motive. "He was a loner, and we're having difficulty finding information about him," school spokesman Larry Hincker said.
Col. Steve Flaherty, superintendent of the Virginia State Police, said it was reasonable to assume that Cho was the shooter in both attacks but that link was not yet definitive.
"There's no evidence of any accomplice at either event, but we're exploring the possibility," he said.
A note was found in Cho's dorm room, the Chicago Tribune reported, which included a list of grievances and rantings against "debauchery" on campus.
The gunman's furious shooting rampage Monday at Virginia Tech has left the school living a nightmare — shocked and horrified over the deaths of 32 students and teachers and wondering how such a massacre could occur.
Twelve people remain hospitalized in stable condition, a Virginia hospital spokesman said Tuesday.
All classes for the remainder of the week have been canceled, Virginia Tech President Charles Steger said.
Steger spent Tuesday morning defending the delay in warning students about the gunman. Some students said their first warning came more than two hours after the first shooting, in an e-mail at 9:26 a.m. By then the second shooting had begun.
"I can understand the anger and the rage," Steger told CBS' The Early Show. But Steger added bluntly, "We believe we have acted appropriately."
Some students bitterly complained they got no warning from the university until an e-mail that arrived more than two hours after the first shots.
"I think the university has blood on their hands because of their lack of action after the first incident," said Billy Bason, 18, who lives on the seventh floor of the dorm.
Student Maurice Hiller said he went to a 9 a.m. class two buildings away from the engineering building, and no warnings were coming over the outdoor public address system on campus at the time.
Everett Good, junior, said of the lack of warning: "I'm trying to figure that out. Someone's head is definitely going to roll over that."
"We were kept in the dark a lot about exactly what was going on," said Andrew Capers Thompson, a 22-year-old graduate student from Walhalla, S.C.
Steger said the university was trying to notify students who were already on-campus, not those who were commuting in.
"We warned the students that we thought were immediately impacted," he told CNN. "We felt that confining them to the classroom was how to keep them safest."
Steger said authorities believed the shooting at the dorm was a domestic dispute and mistakenly thought the gunman had fled the campus.
Katie Couric will anchor The CBS Evening News from Blacksburg, Va., tonight at 6:30 p.m. and there will a one-hour special on the massacre on 48 Hours Tuesday night at 10 p.m.
"We had no reason to suspect any other incident was going to occur," he said.
Steger emphasized that the university closed off the dorm after the first attack and decided to rely on e-mail and other electronic means to spread the word, but said that with 11,000 people driving onto campus first thing in the morning, it was difficult to get the word out.