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Show that the range of $f^*$ is orthogonal complement of the nullspace of $f$. Deduce that the rank of $f$ is equal to the rank of $f^*$, Deduce that the row rank of a square matrix is equal to its column rank.

There are so many technical questions in my workbook I am getting confused here.

Theo Bendit
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user600384
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  • Take them one at a time then. Lumping them all together makes it seem so much harder. For example, you can find an answer to your first question here, though I'd recommend reviewing the definition of adjoint, orthogonal complement, and nullspace, as the result really just falls out from using these three definitions. – Theo Bendit Oct 18 '18 at 02:08
  • I edited your question, adding "$" signs to make the $\LaTeX$ work. Cheers! – Robert Lewis Oct 18 '18 at 02:09

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