This segment explains the relationship between the eigenvalues of matrix R (obtained from QR decomposition) and the eigenvalues of the original matrix A. The speaker clarifies that the eigenvalues of R are the diagonal values, and because post-multiplying by an orthogonal matrix (Q) doesn't change eigenvalues, the eigenvalues of A and R are the same. This is crucial for understanding the convergence of the QR algorithm and its application in finding eigenvalues. QR algorithm iteratively decomposes a matrix (A) into QR factors. Convergence implies QR=RQ, revealing that the eigenvalues of the converged R (upper triangular) are the eigenvalues of A. These are the diagonal entries of R. The proof, detailed next time, uses the fact that conjugation by orthogonal matrices (Q) doesn't change eigenvalues.