1.3 ARRAY OPERATIONS

1.3 ARRAY OPERATIONS

Array operations refer to element-by-element arithmetic operations. Preceding

the linear algebraic matrix operations, * / \ ‘ , by a period (.) indicates an array

or element-by-element operation. Thus, the operators .* , .\ , ./, .^ , represent

element-by-element multiplication, left division, right division, and raising to

the power, respectively. For addition and subtraction, the array and matrix operations

are the same. Thus, + and .+ can be regarded as an array or matrix

addition.

If A1 and B1 are matrices of the same dimensions, then A1.*B1 denotes an array

whose elements are products of the corresponding elements of A1 and B1.

Thus, if

A1 = [2 7 6

8 9 10];

B1 = [6 4 3

2 3 4];

then

C1 = A1.*B1

results in

C1 =

12 28 18

16 27 40

An array operation for left and right division also involves element-by-element

operation. The expressions A1./B1 and A1.\B1 give the quotient of elementby-

element division of matrices A1 and B1. The statementD1 = A1./B1

gives the result

D1 =

0.3333 1.7500 2.0000

4.0000 3.0000 2.5000

and the statement

E1 = A1.\B1

gives

E1 =

3.0000 0.5714 0.5000

0.2500 0.3333 0.4000

The array operation of raising to the power is denoted by .^. The general

statement will be of the form:

q = r1.^s1

If r1 and s1 are matrices of the same dimensions, then the result q is also a matrix

of the same dimensions. For example, if

r1 = [ 7 3 5];

s1 = [ 2 4 3];

then

q1 = r1.^s1

gives the result

q1 =

49 81 125

© 1999

One of the operands can be scalar. For example,

q2 = r1.^2

q3 = (2).^s1

will give

q2 =

49 9 25

and

q3 =

4 16 8

Note that when one of the operands is scalar, the resulting matrix will have the

same dimensions as the matrix operand.