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A matrix $A$ has $m$ rows and $n$ colums, such that $m \leq n$. We know that each row of $A$ has the norm $1$ (the norm of an element $x=(x_1,x_2,...,x_n) \in \mathbb{R}^n$ is $||x||=\sqrt{x_1^2+x_2^2+...+x_n^2}$)) and any two rows are orthogonal (if $y=(y_1,y_2,...,y_n) \in \mathbb{R}^n$ then $x$ and $y$ are orthogonal if their dot product is $0$, i.e. $x_1y_1+x_2y_2+...+x_ny_n=0$. Is the sum of the squares of the minors of order $m$ of $A$ equal $1$? I think that this is true. What I did, was to find out that $A*^tA=I_n$ and I know that the eigenvalues of A have absolute value 1 (they are not necessarily real). Observation: The matrix is not a square matrix. We have $A*^tA=I_n$ but $^tA*A=I_n$ is not equivalent to the first (if this relation holds, then $n\leq m$ which is not given).

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  • $\begingroup$ Does this problem come from a research problem, a homework set or something else? $\endgroup$ Oct 2, 2014 at 15:12
  • $\begingroup$ I had a conversation with one of my friends about orthogonal matrices and he told me about this. In this case, the matrix is not a square matrix, because $m\leq n$ (rectangular), but somehow related.. $\endgroup$
    – user95553
    Oct 2, 2014 at 15:18
  • $\begingroup$ I see. Are you aware of the fact that this site is meant for more or less research level mathematics, whereas math.stackexchange is for all kinds of mathematics? You can find it here: math.stackexchange.com (I am not saying that your question is not suitable here but making sure that you know the situation.) $\endgroup$ Oct 2, 2014 at 15:22
  • $\begingroup$ I posted this here because it's for my own research and any help would be appreciated. Should I delete it? $\endgroup$
    – user95553
    Oct 3, 2014 at 10:07
  • $\begingroup$ If it's related to research in mathematics, try editing your question to provide more context. Then it could be reopened. If it's research in some other field, M.SE might be more suitable, since it has been put on hold as off-topic here. You can also ask the moderators to migrate your post to M.SE (use a flag or a comment), so reposting might not be necessary. $\endgroup$ Oct 3, 2014 at 10:29

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