A diagonalizable matrix is a square matrix that can be expressed in the form of $A = PDP^{-1}$, where $D$ is a diagonal matrix containing the eigenvalues of $A$, and $P$ is a matrix whose columns are the corresponding eigenvectors. This property indicates that the matrix can be transformed into a simpler form, making calculations like exponentiation or solving systems of linear equations much easier. Diagonalizable matrices are crucial in eigendecomposition, as they allow for efficient data analysis and transformations.
congrats on reading the definition of Diagonalizable Matrix. now let's actually learn it.