With the diagonalisation of matrices, we have arrived at the heart of linear algebra. The key to diagonalisation is vectors v not equal to the zero vector with \(A \, v = \lambda \, v\) for a \(\lambda \in {\mathbb K}\) – v is called eigenvector and \(\lambda \) eigenvalue. When diagonalising a matrix \(A \in {\mathbb K}^{n \times n}\) , all eigenvalues of A and a basis of \({\mathbb K}^n\) consisting of eigenvectors are determined.