Diagonalizable matrix

Matrices similar to diagonal matrices

In linear algebra, a square matrix  is called diagonalizable or non-defective if it is similar to a diagonal matrix. That is, if there exists an invertible matrix  and a diagonal matrix such that . This is equivalent to . This property exists for any linear map: for a finite-dimensional vector space , a linear map  is called diagonalizable if there exists an ordered basis of  consisting of eigenvectors of . These definitions are equivalent: if  has a matrix representation as above, then the column vectors of  form a basis consisting of eigenvectors of , and the diagonal entries of  are the corresponding eigenvalues of ; with respect to this eigenvector basis,  is represented by .

This keyword could refer to multiple things. Here are some suggestions: