Cauchy's interlace theorem and lower bounds for the spectral radius (Q1578357)

A new proof is presented for the Cauchy interlace theorem (the theorem states that if a row-column pair is deleted from a real symmetric matrix \(A\), then the eigenvalues of the resulting matrix interlace those of the original ones). The proof comprises the case in which the matrix has distinct eigenvalues and the case of multiple eigenvalues. The lower bounds for the spectral radius of a real symmetric matrix are improved.