HP 50g manual Matrix-vector multiplication, Matrix multiplication

Matrix-vector multiplication

Matrix-vector multiplication is possible only if the number of columns of the matrix is equal to the length of the vector. A couple of examples of matrix- vector multiplication follow:

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. 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

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:

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