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mpower, ^

Matrix power

Syntax

Description

example

C = A^B computes A to the B power and returns the result in C.

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

Examples

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Square a Matrix

Create a 2-by-2 matrix and square it.

A = [1 2; 3 4];
C = A^2
C =

     7    10
    15    22

The syntax A^2 is equivalent to A*A.

Matrix Exponents

Create a 2-by-2 matrix and use it as the exponent for a scalar.

B = [0 1; 1 0];
C = 2^B
C =

    1.2500    0.7500
    0.7500    1.2500

Compute C by first finding the eigenvalues D and eigenvectors V of the matrix B.

[V,D] = eig(B)
V =

   -0.7071    0.7071
    0.7071    0.7071


D =

    -1     0
     0     1

Next, use the formula 2^B = V*2^D/V to compute the power.

C = V*2^D/V
C =

    1.2500    0.7500
    0.7500    1.2500

Input Arguments

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A — Basescalar | matrix

Base, specified as a scalar or matrix. Inputs A and B must be one of the following:

  • Base A is a square matrix and exponent B is a scalar. If B is a positive integer, the power is computed by repeated squaring. For other values of B the calculation involves eigenvalues and eigenvectors.

  • Base A is a scalar and exponent B is a square matrix. The calculation uses eigenvalues and eigenvectors.

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

B — Exponentscalar | matrix

Exponent, specified as a scalar or matrix. Inputs A and B must be one of the following:

  • Base A is a square matrix and exponent B is a scalar. If B is a positive integer, the power is computed by repeated squaring. For other values of B the calculation involves eigenvalues and eigenvectors.

  • Base A is a scalar and exponent B is a square matrix. The calculation uses eigenvalues and eigenvectors.

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

See Also

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