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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In numerical linear algebra, the QR algorithm is an eigenvalue algorithm: that is, a procedure to calculate the eigenvalues and eigenvectors of a matrix. The QR transformation was developed in 1961 by John G.F. Francis (England) and by Vera N. Kublanovskaya (USSR), working independently. The basic idea is to perform a QR decomposition, writing the matrix as a product of an orthogonal matrix and an upper triangular matrix, multiply the factors in the other order, and iterate.