Matrices

This topic includes:

matrix arithmetic: the order of a matrix, types of matrices (row, column, square, diagonal, symmetric, triangular, zero, binary and identity), the transpose of a matrix, and elementary matrix operations (sum, difference, multiplication of a scalar, product and power)
inverse of a matrix, its determinant, and the condition for a matrix to have an inverse
use of matrices to represent numerical information presented in tabular form, and the use of a rule for the aᵢⱼth element of a matrix to construct the matrix
binary and permutation matrices, and their properties and applications
communication and dominance matrices and their use in analysing communication systems and ranking players in round-robin tournaments.

This topic includes:

use of the matrix recurrence relation: initial state matrix, or where is a transition matrix, is a Leslie matrix, and is a column state matrix, to generate a sequence of state matrices (assuming the next state only relies on the current state) informal identification of the equilibrium state matrix in the case of regular transition matrices (no noticeable change from one state matrix to the next state matrix)
use of transition diagrams, their associated transition matrices and state matrices to model the transitions between states in discrete dynamical situations and their application to model and analyse practical situations such as the modelling and analysis of an insect population comprising eggs, juveniles and adults
use of the matrix recurrence relation initial state matrix, to extend modelling to populations that include culling and restocking.