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power, .^

Element-wise power



C = A.^B raises each element of A to the corresponding powers in B. The sizes of A and B must be the same or be compatible.

If the sizes of A and B are compatible, then the two arrays implicitly expand to match each other. For example, if one of A or B is a scalar, then the scalar is combined with each element of the other array. Also, vectors with different orientations (one row vector and one column vector) implicitly expand to form a matrix.

C = power(A,B) is an alternate way to execute A.^B, but is rarely used. It enables operator overloading for classes.


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Create a vector, A, and square each element.

A = 1:5;
C = A.^2
C = 1×5

     1     4     9    16    25

Create a matrix, A, and take the inverse of each element.

A = [1 2 3; 4 5 6; 7 8 9];
C = A.^-1
C = 3×3

    1.0000    0.5000    0.3333
    0.2500    0.2000    0.1667
    0.1429    0.1250    0.1111

An inversion of the elements is not equal to the inverse of the matrix, which is instead written A^-1 or inv(A).

Create a 1-by-2 row vector and a 3-by-1 column vector and raise the row vector to the power of the column vector.

a = [2 3];
b = (1:3)';
ans = 3×2

     2     3
     4     9
     8    27

The result is a 3-by-2 matrix, where each (i,j) element in the matrix is equal to a(j) .^ b(i):

a=[a1a2],b=[b1b2b3],          a.ˆb=[a1b1a2b1a1b2a2b2a1b3a2b3].

Calculate the roots of -1 to the 1/3 power.

A = -1;
B = 1/3;
C = A.^B
C = 0.5000 + 0.8660i

For negative base A and noninteger B, the power function returns complex results.

Use the nthroot function to obtain the real roots.

C = nthroot(A,3)
C = -1

Input Arguments

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Operands, specified as scalars, vectors, matrices, or multidimensional arrays. A and B must either be the same size or have sizes that are compatible (for example, A is an M-by-N matrix and B is a scalar or 1-by-N row vector). For more information, see Compatible Array Sizes for Basic Operations.

  • Operands with an integer data type cannot be complex.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char
Complex Number Support: Yes

More About

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IEEE Compliance

For real inputs, power has a few behaviors that differ from those recommended in the IEEE®-754 Standard.








Extended Capabilities

Version History

Introduced before R2006a

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Behavior changed in R2016b