Students interested in learning an innovative way to make solving a complex mathematical problem faster and easier crowded into the Aula Magna at Florida Polytechnic University on Jan. 31.
Dr. Udita Katugampola, an assistant professor of mathematics, shared with the students a fast and nontraditional approach he has developed to find the eigenvector of a matrix. He explained how his method can take the process from 10 to 15 minutes for complex matrices to under a minute.
“It is very interesting to see someone like Dr. K present this,” said senior Stephen Boyle, who is majoring in mechanical engineering. “To see the way he thinks about things is very different compared to other people. He sees mathematics almost like another animal – second nature almost.”
Katugampola said he was grading final examinations in December 2019 when he began to try to figure out why some students struggled with the concept and erred on their exams.
“I was thinking about it and those numbers were in my head for a day or two when I suddenly realized this,” Katugampola said. “All of a sudden I thought, ‘Oh, man. This works.’”
According to Katugampola, the simplified method for finding eigenvectors will make it easier for students to understand many new concepts because they will only need knowledge of college algebra as a foundation. The method can be used across many disciplines, as the eigenvectors are used in things like robotics, computer science, image processing, finding chemical reactions, and even the Google search engine.
“We are privileged,” said Boyle, from Brandon, Florida. “Most universities don’t have access like this and it’s really cool that this is going to be implemented in our teaching in the next few months while other universities will have to wait for a new book or paper to be published on it.”
The mathematics department at Florida Poly will soon begin incorporating Katugampola’s method into regular instruction.
Katugampola submitted a 40-page paper detailing this method to a top mathematics journal for consideration. He is also planning several national and international research talks to disseminate his findings and discuss them for further development.
“Recently, Dr. Terence Tao and his collaborators at UCLA found another method to determine eigenvectors for Hermitian matrices, but our method works for pretty much any matrix, Hermitian or not,” Katugampola said.
Katugampola said his method uses simple subtraction to find those eigenvectors and hopes students will remember it through the mnemonic, “Find your puppy at your neighbor’s,” meaning the eigenvector is in the other matrix.
Seminar attendees said they were grateful to learn Katugampola’s method.
“Him being able to teach us this method will save us a lot of time,” said Sandra Davis, a senior majoring in mechanical engineering from Plant City, Florida. “His approach to math is always so different, and he always tries to give us extra information and find the easiest approaches for us.”
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