HP 48gII for, cij = ∑aik ⋅bkj , for i = 1,2,K, m; j = 1,2,K, n

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:

Term-by-term multiplication

Term-by-term multiplication of two matrices of the same dimensions is possible through the use of function HADAMARD. The result is, of course, another matrix of the same dimensions. This function is available through Function catalog (‚N), or through the MATRICES/OPERATIONS sub-menu („Ø). Applications of function HADAMARD are presented next:

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