Matrix notation, types and construction
Linear operations on matrices
Matrix products, powers and permutations
Determinants, inverses and matrix equations
Applications of matrix products
Communication and dominance matrices
Construct the transpose of a matrix by interchanging row and column addresses Test the defining zero and symmetry conditions for diagonal, triangular and identity matrices Construct a matrix from a labelled table preserving the declared row and column categories Construct a matrix by evaluating an entry rule in the one-based row and column indices State the order of a matrix as rows × columns Address an element by row and column subscripts, in both directions Classify row, column, square, symmetric and zero matrices Read a labelled data matrix and its row and column totals Decide matrix equality from equal order and equal corresponding entries Decide whether a sum or difference of matrices is defined Add or subtract matrices entry by corresponding entry Use the zero matrix's behaviour under addition and subtraction Solve for unknown entries by equating corresponding positions Multiply every entry of a matrix by a scalar Evaluate a combination of scalar multiples of two matrices Recognise a binary matrix and decide whether a square binary matrix is a permutation matrix Construct or apply a permutation matrix that rearranges a row or column matrix in a stated order Undo a permutation using P^(-1) = P^T without assuming every permutation matrix is self-inverse Test whether a matrix product is defined from the inner numbers State a matrix product's order from the outer numbers Multiply matrices by pairing rows with columns and summing the products Recognise that matrix multiplication is not commutative Raise a square matrix to a power by repeated multiplication Use the identity matrix and its unchanged products Use technology to obtain and interpret the exact determinant of a square matrix beyond order two Use technology to obtain an exact inverse beyond order two and verify it by multiplication Isolate an unknown matrix in additive, left-product or right-product matrix equations Calculate the determinant of a 2 × 2 matrix Define the inverse as the matrix that multiplies to the identity Apply the 2 × 2 inverse rule Recognise that a matrix with determinant zero has no inverse Solve a matrix equation by left-multiplying by the inverse Set up a matrix product that answers a stated question Interpret the entries of a matrix product in context Extract row or column totals with a ones matrix Identify a leading-diagonal entry of a communication-matrix power as a route returning to its starting vertex Encode a directed comparison relation as a square binary matrix under one source-to-target convention Rank participants from row totals of a declared sum of dominance matrix powers, retaining ties Build the connection matrix of a network Identify the network a connection matrix describes Link connection-matrix symmetry to two-way connections Count the connections at a vertex from a row or column sum Count two-step routes from the square of the connection matrix