mpower, ^

Matrix power

Syntax

C = A^B

C = mpower(A,B)

Description

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

collapse all

Square a Matrix

Open Live Script

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

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

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

Matrix Exponents

Open Live Script

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

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

C = 2×2

    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 = 2×2

   -0.7071    0.7071
    0.7071    0.7071

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

C = V*2^D/V

C = 2×2

    1.2500    0.7500
    0.7500    1.2500

Input Arguments

collapse all

`A`, `B` — Operands
scalar | matrix

Operands, specified as scalars or matrices. Inputs A and B must be one of the following combinations:

Base A and exponent B are both scalars, in which case A^B is equivalent to A.^B.
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.

Operands with an integer data type cannot be complex.

Tips

MATLAB^® computes X^(-1) and inv(X) in the same manner, and both are subject to the same limitations. For more information, see inv.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

If A is a 2-by-2 or larger matrix and B is Inf or -Inf, then A^B returns a matrix of NaN values.
For A^b, if b is a noninteger scalar, then at least one of A or b must be complex.
Code generation does not support sparse matrix inputs for this function.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

If A is a 2-by-2 or larger matrix and B is Inf or -Inf, then A^B returns a matrix of NaN values.
For A^b, if b is a noninteger scalar, then at least one of A or b must be complex.
Code generation does not support sparse matrix inputs for this function.

HDL Code Generation
Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

Both inputs must be scalar, and the exponent input, k, must be an integer.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

Usage notes and limitations:

Both A and B must be scalar.

For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Documentation

mpower, ^

Syntax

Description

Examples

Square a Matrix

Matrix Exponents

Input Arguments

`A`, `B` — Operands
scalar | matrix

Tips

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

HDL Code Generation
Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

See Also

Topics

MATLAB Documentation

Support

Documentation

mpower, ^

Syntax

Description

Examples

Square a Matrix

Matrix Exponents

Input Arguments

A, B — Operands scalar | matrix

Tips

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

HDL Code Generation Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

GPU Arrays Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Distributed Arrays Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

See Also

Topics

MATLAB Documentation

Support

`A`, `B` — Operands
scalar | matrix

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

HDL Code Generation
Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.