An eigenbasis for a linear transformation 
is a basis
of 
consisting entirely of eigenvectors
of 
. Equivalently, a square
matrix has an eigenbasis iff it is diagonalizable.
If the columns of a matrix 
are the vectors in an eigenbasis and the corresponding eigenvalues form the diagonal
matrix 
,
then
 |
A real symmetric matrix has an orthonormal basis of eigenvectors, meaning that the basis vectors are pairwise orthogonal and each has unit length. A complex normal matrix also has an orthonormal basis of eigenvectors.
