The QR algorithm is a numerical method used to find the eigenvalues and eigenvectors of a matrix by decomposing it into an orthogonal matrix Q and an upper triangular matrix R. This iterative process allows for the approximation of eigenvalues, which are crucial in various applications such as stability analysis and principal component analysis. Understanding the QR algorithm is key for leveraging eigenvalues and eigenvectors in solving real-world problems across engineering and data science.
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