What is matrix diagonalisation?

• A?non-zero,?square?matrix is considered to be?diagonal?if all elements?not?along its leading diagonal?are?zero
• You will only need to consider matrices with?real,?distinct?eigenvalues
  • If there is only one eigenvalue, the matrix is either already diagonalised or cannot be diagonalised
  • Diagonalisation of matrices with complex or imaginary eigenvalues is outside the scope of the course

One of the main applications of diagonalising a matrix is to make it easy to find?powers?of the matrix, which is useful when modelling transient situations such as the movement of populations between two towns.

How can the diagonalised matrix be used to find higher powers of the original matrix?