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Adam Gal
Adam Gal
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Let $A$ be a $m\times n$ matrix with $n\sim m^2$ and with rank $m$, and $C$ a $n\times n$ permutation matrix of order 2. Is it true that $ACA^T$ is always invertible? or in some special cases?

If it helps: you may assume $A$ is in row echelon form with all entries being 0 or 1.

Let $A$ be a $m\times n$ matrix with $n\sim m^2$ and with rank $m$, and $C$ a $n\times n$ permutation matrix of order 2. Is it true that $ACA^T$ is always invertible? or in some special cases?

Let $A$ be a $m\times n$ matrix with $n\sim m^2$ and with rank $m$, and $C$ a $n\times n$ permutation matrix of order 2. Is it true that $ACA^T$ is always invertible? or in some special cases?

If it helps: you may assume $A$ is in row echelon form with all entries being 0 or 1.

Source Link
Adam Gal
Adam Gal
  • 700
  • 4
  • 19

rank of $ACA^T$

Let $A$ be a $m\times n$ matrix with $n\sim m^2$ and with rank $m$, and $C$ a $n\times n$ permutation matrix of order 2. Is it true that $ACA^T$ is always invertible? or in some special cases?