Let $A$ be a square matrix of size $n \times n$ ($n>2$) and let $B$ be $A$ if we delete the last row and column (size $(n-1) \times (n-1)$). Let $\sigma (A)$ be the least singular value of $A$ and $\sigma(B)$ the least singular value of $B$. Is it true that $\sigma(A) \leq \sigma(B)$?


I have seen the interlacing theorem but I am not sure if it can be used for non-symmetric matrices. My main concern is example 2 in 17-12 of <http://math.ecnu.edu.cn/~jypan/Teaching/books/SVD.pdf>



On the least singular values
No: $\begin{pmatrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\0 & 1 & 0 \end{pmatrix}$


