The conversation between human and AI assistant.
How do I solve the problem: [math] A=\begin{pmatrix} -2 &4 \\   -5& 7 \end{pmatrix}, A^{n}=? [/math]?
That makes sense, but can you explain what diagonalizing a matrix means?
Diagonalizing a matrix involves finding a matrix P such that P^-1AP is a diagonal matrix D. The diagonal matrix D then consists of the eigenvalues of A, while the columns of P are the eigenvectors of A. Does that help?