Why do the non-zero singularvalues of a matrix keep increasing in magnitude as more redundant rows are added to it Let us consider a matrix $\mathbf{A}\in\mathbb{R}^{n\times n}$ such that rank of the matrix is $n$. If we do the singular value decomposition(SVD) of this matrix, we'll get $4$ non-zero singular values. Now let us add more rows to A such that the rank of $\mathbf{A}$ stays constant at $n$. Every time we add a row, we perform SVD on the augmented matrix. We see that as we keep on adding more redundant rows to $\mathbf{A}$, the non-zero singular values keep on shifting to right i.e. their value keeps on increasing. Can anyone explain this phenomena to me? Is it due to eigenvalue repulsion?

Recall that the squares of the singular values are the eigenvalues of $A^*A$. So $$ B = \begin{pmatrix} A \\\ b \end{pmatrix} \implies B^*B = A^*A+ b^*b , $$ and the eigenvalues increase (though perhaps not strictly) by the min-max principle.