A proof assistant is software used for creating and checking formal proofs; examples include Coq and HOL. This tag is not to be used for requesting assistance on finding proofs.

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Complexity of reordering a matrix which consists independent sub matrices

Introduction: Given a matrix A of a $k$ regular graph G. The matrix A can be divided into 4 sub matrices based on adjacency of vertex $x \in G$. $A_x$ is the symmetric matrix of the graph $(G-x)$, ...
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Changes in singular Values of matrix when adding row

I know that if a column is added to a matrix then the matrix largest signular value increases and the smallest singular value decreases. That is: Given matrix $A \in R^{m \text{x} n}$, $m>n$, and ...