issymmetric

Determine if matrix is symmetric or skew-symmetric

Syntax

tf = issymmetric(A)

tf = issymmetric(A,skewOption)

Description

tf = issymmetric(A)returns logical1(true) if square matrixAissymmetric; otherwise, it returns logical0(false).

example

tf = issymmetric(A，skewOption)specifies the type of the test. SpecifyskewOptionas'skew'to determine ifAisskew-symmetric.

Examples

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Test if Hermitian Matrix Is Symmetric

Open Live Script

Create a 3-by-3 matrix.

A = [1 0 1i; 0 1 0;-1i 0 1]

A =3×3 complex1.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 1.0000i 0.0000 + 0.0000i 1.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 1.0000i 0.0000 + 0.0000i 1.0000 + 0.0000i

The matrix is Hermitian and has a real-valued diagonal.

Test whether the matrix is symmetric.

tf = issymmetric(A)

tf =logical0

The result is logical0(false) becauseAis not symmetric. In this case,Ais equal to its complex conjugate transpose,一个“，but not its nonconjugate transpose,A.'.

Change the element inA(3,1)to be1i.

A(3,1) = 1i;

Determine whether the modified matrix is symmetric.

tf = issymmetric(A)

tf =logical1

The matrix,A，is now symmetric because it is equal to its nonconjugate transpose,A.'.

Test if Matrix Is Skew-Symmetric

Open Live Script

Create a 4-by-4 matrix.

A = [0 1 -2 5; -1 0 3 -4; 2 -3 0 6; -5 4 -6 0]

A =4×40 1 -2 5 -1 0 3 -4 2 -3 0 6 -5 4 -6 0

The matrix is real and has a diagonal of zeros.

SpecifyskewOptionas'skew'to determine whether the matrix is skew-symmetric.

tf = issymmetric(A,'skew')

tf =logical1

The matrix,A，is skew-symmetric since it is equal to the negation of its nonconjugate transpose,-A.'.

Input Arguments

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`A`—Input matrix
numeric matrix

Input matrix, specified as a numeric matrix. IfAis not square, thenissymmetricreturns logical0(false).

Data Types:single|double|logical
Complex Number Support:Yes

`skewOption`—Test type
`'nonskew'`(default) |`'skew'`

Test type, specified as'nonskew'or'skew'. Specify'skew'to test whetherAisskew-symmetric.

More About

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Symmetric Matrix

A square matrix,A，is symmetric if it is equal to its nonconjugate transpose,A = A.'.
In terms of the matrix elements, this means that

$a_{i ， j} = a_{j ， i} .$
因为真正的矩阵是联合国affected by complex conjugation, a real matrix that is symmetric is also Hermitian. For example, the matrix

$A = [\begin{matrix} \begin{matrix} \begin{matrix} 1 \\ 0 \end{matrix} & \begin{matrix} 0 \\ 2 \end{matrix} \end{matrix} & \begin{matrix} 1 \\ 0 \end{matrix} \\ \begin{matrix} 1 & 0 \end{matrix} & 1 \end{matrix}]$

is both symmetric and Hermitian.

Skew-Symmetric Matrix

A square matrix,A，is skew-symmetric if it is equal to the negation of its nonconjugate transpose,A = -A.'.
In terms of the matrix elements, this means that

$a_{i ， j} = - a_{j ， i} .$
因为真正的矩阵是联合国affected by complex conjugation, a real matrix that is skew-symmetric is also skew-Hermitian. For example, the matrix

$A = [\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}]$

is both skew-symmetric and skew-Hermitian.

Extended Capabilities

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

Usage notes and limitations:

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:

Code generation does not support sparse matrix inputs for this function.

Thread-Based Environment
Run code in the background using MATLAB®`backgroundPool`or accelerate code with Parallel Computing Toolbox™`ThreadPool`.

This function fully supports thread-based environments. For more information, seeRun MATLAB Functions in Thread-Based Environment.

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, seeRun MATLAB Functions on a GPU(Parallel Computing Toolbox).

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

This function fully supports distributed arrays. For more information, seeRun MATLAB Functions with Distributed Arrays(Parallel Computing Toolbox).

Version History

Introduced in R2014a

issymmetric

Syntax

Description

Examples

Test if Hermitian Matrix Is Symmetric

Test if Matrix Is Skew-Symmetric

Input Arguments

A—Input matrixnumeric matrix

skewOption—Test type'nonskew'(default) |'skew'

More About

Symmetric Matrix

Skew-Symmetric Matrix

Extended Capabilities

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

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

Thread-Based EnvironmentRun code in the background using MATLAB®backgroundPoolor accelerate code with Parallel Computing Toolbox™ThreadPool.

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

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

Version History

See Also

`A`—Input matrix
numeric matrix

`skewOption`—Test type
`'nonskew'`(default) |`'skew'`

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

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

Thread-Based Environment
Run code in the background using MATLAB®`backgroundPool`or accelerate code with Parallel Computing Toolbox™`ThreadPool`.

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™.