Matrix Exponentiation

Matrix exponentiation involves raising a matrix to a power, much like multiplying a number by itself multiple times. It's a powerful tool for solving systems of linear equations, modeling processes like population growth or network flows, and computing repeated transformations efficiently. Instead of multiplying the matrix by itself repeatedly, algorithms use techniques like binary exponentiation to quickly compute large powers. This method leverages the properties of matrices and their multiplication, enabling complex calculations to be done more efficiently, especially for large exponents, making it fundamental in fields such as computer science, physics, and engineering.