How to Use .^ Operator in MATLAB for Element-wise Power

In MATLAB, the .^ operator performs element-wise power, raising each element of an array to the specified power individually. Use A .^ B where A and B are arrays or scalars of compatible sizes to compute powers element by element.

Syntax

The syntax for element-wise power in MATLAB is A .^ B.

• A: Base array or scalar.
• .^: Element-wise power operator.
• B: Exponent array or scalar, must be compatible in size with A.

This operator raises each element of A to the corresponding power in B.

matlab

C = A .^ B;

Example

This example shows how to square each element of an array and how to raise elements to different powers.

matlab

A = [1, 2, 3; 4, 5, 6];
B = 2; % scalar exponent
C = A .^ B;

D = [1, 2, 3; 2, 3, 4]; % element-wise exponents
E = A .^ D;

C
E

Output

C =
     1     4     9
    16    25    36

E =
     1     4    27
    16   125   1296

Common Pitfalls

One common mistake is using ^ instead of .^ when working with arrays. The ^ operator performs matrix power, which requires a square matrix and does not operate element-wise.

Another pitfall is mismatched array sizes for A and B when both are arrays. They must be the same size or compatible for broadcasting.

matlab

A = [1, 2; 3, 4];
B = [2, 3; 4, 5];

% Wrong: matrix power (only for square matrices)
% C_wrong = A ^ B; % This will cause an error

% Correct: element-wise power
C_right = A .^ B;

Output

C_right =
     1     8
    81  1024

Quick Reference

Operator	Description	Example
.^	Element-wise power	A .^ 2 squares each element of A
^	Matrix power (square matrices only)	A ^ 2 multiplies A by itself
.*	Element-wise multiplication	A .* B multiplies elements of A and B
*	Matrix multiplication	A * B multiplies matrices A and B

Key Takeaways

Use .^ to raise each element of an array to a power individually in MATLAB.

The ^ operator is for matrix power and requires square matrices.

Ensure arrays used with .^ have compatible sizes or use scalars.

Element-wise operations are essential for array-by-array calculations in MATLAB.