HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 330

Vector-matrix multiplication, on the other hand, is not defined. This multiplication can be performed, however, as a special case of matrix multiplication as defined next. Matrix multiplication Matrix multiplication is defined by Cm×n = Am×p⋅Bp×n, where A = [aij]m×p, B = [bij]p×n, and C = [cij]m×n. Notice that matrix multiplication is only possible if the number of columns in the first operand is equal to the number of rows of the second operand. The general term in the product, cij, is defined as p ∑ cij = aik ⋅bkj , for i = 1,2,K, m; j = 1,2,K, n. k =1 This is the same as saying that the element in the i-th row and j-th column of the product, C, results from multiplying term-by-term the i-th row of A with the jth column of B, and adding the products together. Matrix multiplication is not commutative, i.e., in general, A⋅B ≠ B⋅A. Furthermore, one of the multiplications may not even exist. The following screen shots show the results of multiplications of the matrices that we stored earlier: The matrix-vector multiplication introduced in the previous section can be thought of as the product of a matrix m×n with a matrix n×1 (i.e., a column vector) resulting in an m×1 matrix (i.e., another vector). To verify this assertion check the examples presented in the previous section. Thus, the vectors defined in Chapter 9 are basically column vectors for the purpose of matrix multiplication. Page 11-4