Matrices — Formula Sheet

A = [a_ij]_(m×n)

Number of elements in an m×n matrix = mn

Order of a matrix = m×n

Two matrices A and B are equal if A_ij = B_ij for all i, j

(A+B)_ij = A_ij + B_ij

(A-B)_ij = A_ij - B_ij

(kA)_ij = kA_ij

(AB)_ij = Σ(k=1 to n) A_ik B_kj

Order of AB = m×p

I_m A = A = A I_n

A^0 = I

(AB)C = A(BC)

(A^T)_ij = A_ji

(A^T)^T = A

(A+B)^T = A^T + B^T

(kA)^T = kA^T

(AB)^T = B^T A^T

Order of a matrix = number of rows × number of columns