Hp 49g+ User Manual download pdf (Page 326)

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101

Page 11-4

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 C

= A

⋅B

, where A = [a

]

, B =

]

, and C = [c

]

. 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, c

, is defined as

.,,2,1;,,2,1,

njmiforbac

kjikij

KK ==⋅=

∑

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 j-

th 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.

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