A real <normal matrix> satisfies $MM^T=M^TM$. For a <symmetric matrix>, $M^T=M$ and both products equal $M^2$. For an <antisymmetric matrix>, $M^T=-M$ and both equal $-M^2$. For an <orthogonal matrix>, both products are the identity. Thus \b[each of the three classes consists of normal matrices].

Solution

Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2005 / Paper 2 / 9 / a / Solution

 Solution (source code)