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One key operation in a deep neural network involves the use of linear algebra to perform matrix multiplication, which transforms data as it is passed from layer to layer.

With calculations based on linear algebra, the research team demonstrated that -- analogous to radioactivity in atomic nuclei -- a magnetic quiver can decay into a more stable state or fission into two separate quivers.

The Julia Programming Language, a popular language for scientific computing that is also used in MIT's introductory linear algebra classes, offers many tools that make it invaluable for constructing such generative models, Schäfer adds.

Thankfully, the results of computer simulations, mean-field theory, a statistical theory of particles, and mathematical proofs based on linear algebra were all consistent.

To spot patterns in this massive amount of data, companies use common methods from linear algebra, such as singular value decomposition or principal component analysis.