Linear Algebra: Orthogonal matrices

[Niles]

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.

 

[micromass]

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