Linear Algebra: Orthogonal matrices

Niles
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Homework Statement


Hi

A matrix M has an inverse iff it is of full column and row rank, and row rank = column rank. Since any orthogonal matrix has full column rank, does that imply that non-singular matrices are orthogonal as well?

Cheers,
Niles.
 
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No, we have that orthogonal => full column rank. But we don't have the converse. There are non-singular matrices which are not orthogonal.
 

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