matrix diagonalisations

Matrix diagonalization is a process in linear algebra where a square matrix is transformed into a simpler form called a diagonal matrix, using a similarity transformation. This involves finding its eigenvalues (special numbers associated with the matrix) and eigenvectors (directions that remain unchanged under the transformation). When a matrix is diagonalized, computations like powers or functions of the matrix become easier because diagonal matrices have non-zero entries only on their main diagonal. Essentially, diagonalization reveals the underlying structure of the matrix, simplifying complex calculations and providing deeper insights into the system it represents.