2 to a matrix. I calculate two to the power of a matrix using tools from linear algebra, more precisely diagonalization and eigenvalues and eigenvectors. This is related to matrix exponentials and logarithms, which are used to solve systems of differential equations and decouple particles. This is useful for college calculus and linear algebra students and anyone interested in data science. I also give a formula similar to the geometric series, and I'm wondering if this is useful in computer science and binary integer representations.

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