Newsletter: UP Mathematician Develops Framework to Describe Complex Quantum Operators

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By: Eunice Jean C. Patron

The plot of a time-frequency shifted Gausssian function, an example of a wavelet. A substantial effort in harmonic analysis is devoted to the decomposition of signals in terms of wavelets. (Photo credit: Dr. Arvin Lamando)

Mathematicians Dr. Arvin Lamando of the University of the Philippines – Diliman College of Science’s Institute of Mathematics (UPD-CS IM) and Dr. Henry McNulty of the Norwegian University of Science and Technology have found a new way to understand mathematical “machines” called operators, which are key to quantum mechanics and signal processing. Their study shows that even the most intricate of these operators can be broken down into simpler parts and then reconstructed, offering new insights into quantum systems and technologies.

Newsletter: UPD-CS Mathematicians Introduce Innovative Matrix Decomposition Framework

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By: Eunice Jean C. Patron

Matrix decomposition is an area of linear algebra which is focused on expressing a matrix as a product of matrices with prescribed properties. (Photo credit: Merino et al., 2024)

Imagine discovering an ancient treasure chest sealed with a complex dual-lock mechanism, requiring two keys that must work together in a precise way. A matrix—a rectangular array of numbers—is like a locked chest holding valuable information that helps us understand the world around us. Matrices need keys like decompositions, which break them down into simpler components while preserving their essential properties, to help us understand them better. At times, special kinds of decompositions are required to have a deeper understanding of matrices.