MATLAB - Array Multiplication

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Array multiplication in MATLAB involves performing operations on arrays of numbers.

Element-wise multiplication is used when you want to multiply corresponding elements of two arrays together. This type of multiplication is denoted using the .* operator.

The arrays being multiplied must have the same dimensions. Each element in the resulting array is obtained by multiplying the corresponding elements from the original arrays.

Syntax

X = A.*B
X = times(A,B)

X = A.*B performs array multiplication between A and B by calculating the product of their corresponding elements. It's important to ensure that A and B have either identical sizes or sizes that are compatible for this operation.

The usage of C = times(A,B) as an alternative method to compute A.*B exists, although it's infrequently employed. This approach allows for operator overloading in classes.

Example 1

Multiplying two vectors A and B.

A = [1 2 3]
B = [4 5 6]
X = A.*B

When you execute the same in matlab command window −

A =

     1     2     3

B =

     4     5     6

X =

     4    10    18

Example 2

Let us try another example by using a matrix of 2x3 as shown below −

A = [1, 2, 3; 4, 5, 6]
B = [2, 2, 2; 3, 3, 3]
C = A .* B

When you execute the same in matlab command window the output is −

A =

     1     2     3
     4     5     6

B =

     2     2     2
     3     3     3

C =

     2     4     6
    12    15    18

The matrix C is also the same size as of A and B.

Let us now try to make use of the times() method for the above examples we have tried using .*.

Example 3

Multiplying two vectors A and B using the times() method.

A = [1 2 3]
B = [4 5 6]
X = times(A,B)

When you execute the same in matlab command window −

A =

     1     2     3

B =

     4     5     6

X =

     4    10    18

Example 4

Let us try another example by using a matrix of 2x3 but will multiply them using the times() method.

A = [1, 2, 3; 4, 5, 6]
B = [2, 2, 2; 3, 3, 3]
C = times(A,B)

When you execute the same in matlab command window −

A =

     1     2     3
     4     5     6

B =

     2     2     2
     3     3     3

C =

     2     4     6
    12    15    18

Multiply Row and Column Vectors

The row vector with dimensions 1-by-3 and the column vector with dimensions 4-by-1 are multiplied in the example below, resulting in the creation of a 4-by-3 matrix.

a = 1:3
b = (1:4)'
result_matrix = a .* b

In this example, 'a' is the row vector [1, 2, 3], and 'b' is the column vector . The ' operator is the transpose operator. When applied to a matrix or an array, it flips the rows and columns, effectively transforming rows into columns and columns into rows.

The expression (1:4) generates the row vector [1, 2, 3, 4].Applying the transpose operator ' to the row vector converts it into a column vector −

b =

     1
     2
     3
     4

When these vectors are multiplied element-wise, the resulting matrix 'result_matrix' will be −

a =

   1     2     3

b =

   1
   2
   3
   4

result_matrix =

   1     2     3
   2     4     6
   3     6     9
   4     8    12