Element-wise operations (.*, ./, .^) in MATLAB - Step-by-Step Execution

Concept Flow - Element-wise operations (.*, ./, .^)

Start with two arrays

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Choose element-wise operator

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Apply operator to each pair of elements

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Create new array with results

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End

Element-wise operations apply the chosen operator to each matching element of two arrays, producing a new array of the same size.

Execution Sample

MATLAB

A = [1 2 3];
B = [4 5 6];
C = A .* B;
D = A ./ B;
E = A .^ 2;

This code multiplies, divides, and raises elements of arrays A and B element-wise.

Execution Table

Step	Operation	Elements Involved	Result Element	Result Array State
1	Multiply element 1	A(1)=1, B(1)=4	1*4=4	[4 _ _]
2	Multiply element 2	A(2)=2, B(2)=5	2*5=10	[4 10 _]
3	Multiply element 3	A(3)=3, B(3)=6	3*6=18	[4 10 18]
4	Divide element 1	A(1)=1, B(1)=4	1/4=0.25	[0.25 _ _]
5	Divide element 2	A(2)=2, B(2)=5	2/5=0.4	[0.25 0.4 _]
6	Divide element 3	A(3)=3, B(3)=6	3/6=0.5	[0.25 0.4 0.5]
7	Power element 1	A(1)=1, exponent=2	1^2=1	[1 _ _]
8	Power element 2	A(2)=2, exponent=2	2^2=4	[1 4 _]
9	Power element 3	A(3)=3, exponent=2	3^2=9	[1 4 9]

💡 All elements processed for each operation, arrays fully computed.

Variable Tracker

Variable	Start	After Step 3	After Step 6	After Step 9
A	[1 2 3]	[1 2 3]	[1 2 3]	[1 2 3]
B	[4 5 6]	[4 5 6]	[4 5 6]	[4 5 6]
C (A.*B)	[]	[4 10 18]	[4 10 18]	[4 10 18]
D (A./B)	[]	[]	[0.25 0.4 0.5]	[0.25 0.4 0.5]
E (A.^2)	[]	[]	[]	[1 4 9]

Key Moments - 3 Insights

Why do we use a dot before the operator like .* instead of just *?

The dot means the operation is done element by element, not matrix multiplication. See steps 1-3 in execution_table where each element multiplies separately.

Can we use element-wise operators on arrays of different sizes?

No, arrays must be the same size or compatible for broadcasting. Here, A and B have the same size, so element-wise operations work as shown in all steps.

What happens if we forget the dot and write A * B?

Without the dot, MATLAB does matrix multiplication, which is different and may cause errors if sizes don't match. Our example uses .* to multiply elements individually (see execution_table).

Visual Quiz - 3 Questions

Look at the execution_table, what is the value of C after step 2?

A [4 _ _]

B [_ 10 _]

C [4 10 _]

D [1 2 3]

💡 Hint

Check the 'Result Array State' column at step 2 for C (A.*B).

At which step does the division operation finish computing all elements?

A Step 3

B Step 6

C Step 9

D Step 1

💡 Hint

Look for the last step where 'Divide element' appears in the 'Operation' column.

If we change A to [2 4 6], what will be the value of E after step 9?

A [4 16 36]

B [1 4 9]

C [2 4 6]

D [8 16 36]

💡 Hint

E is A.^2, so square each element of A. Check variable_tracker for E's final values.

Concept Snapshot

Element-wise operations use a dot before the operator: .* for multiply, ./ for divide, .^ for power.
They apply the operation to each pair of elements in arrays of the same size.
Result is a new array with each element computed separately.
Without the dot, MATLAB does matrix operations, which are different.
Always ensure arrays are compatible sizes for element-wise operations.

Full Transcript

This lesson shows how MATLAB performs element-wise operations using the dot operators: .*, ./, and .^. Starting with two arrays A and B, each element in A is combined with the corresponding element in B using the chosen operator. For example, A .* B multiplies each element of A by the matching element of B, producing a new array C. The execution table traces each step: multiplying, dividing, and powering elements one by one. The variable tracker shows how arrays C, D, and E build up their values after each step. Key points include why the dot is needed to do element-wise operations instead of matrix operations, and that arrays must be the same size. The quiz questions check understanding of intermediate results and effects of changing inputs. This visual step-by-step helps beginners see exactly how element-wise operations work in MATLAB.