Nonsymmetric matrix
= Nonsymmetric matrix
{title2=$A^T\ne A$}
A nonsymmetric matrix is a square <matrix> unequal to its <transpose>. Its right <eigenvectors> need not be <orthogonal>, and it need not be a <diagonalizable matrix>. For instance, $A=\begin{pmatrix}1&1\\0&2\end{pmatrix}$ has <eigenvectors> $(1,0)^T$ and $(1,1)^T$ for its distinct <eigenvalues>. A starting <vector> $(1,0)^T$ has nonzero <inner product> with $(1,1)^T$ but zero coefficient in that direction in the <eigenbasis>. This is why <power iteration> and <inverse iteration> require a nonzero spectral component rather than an ordinary nonorthogonality test in the general case.