issymmetric
Determine if matrix is symmetric or skew-symmetric
Description
tf = issymmetric(
returns logical
A
)1
(true
) if A
is a
symmetric matrix.
Otherwise, it returns logical 0
(false
).
tf = issymmetric(
specifies the type of the test. Specify A
,skewOption
)skewOption
as
"skew"
to determine if A
is skew-symmetric.
Examples
Test If Hermitian Matrix Is Symmetric
Create a 3-by-3 matrix.
A = [1 0 1i; 0 1 0;-1i 0 1]
A = 3×3 complex
1.0000 + 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 if the matrix is symmetric.
tf = issymmetric(A)
tf = logical
0
The matrix A
is not symmetric because it is equal to its complex conjugate transpose, A'
, but not its nonconjugate transpose, A.'
.
Change the element in A(3,1)
to 1i
.
A(3,1) = 1i;
Test if the modified matrix is symmetric.
tf = issymmetric(A)
tf = logical
1
The matrix A
is now symmetric because it is equal to its nonconjugate transpose, A.'
.
Test If Matrix Is Skew-Symmetric
Create a 4-by-4 matrix.
A = [0 1 -2 5; -1 0 3 -4; 2 -3 0 6; -5 4 -6 0]
A = 4×4
0 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.
Test if the matrix is skew-symmetric by specifying the test type as "skew"
.
tf = issymmetric(A,"skew")
tf = logical
1
The matrix A
is skew-symmetric because it is equal to the negation of its nonconjugate transpose, -A.'
.
Input Arguments
A
— Input array
array
Input array. If A
is not a square matrix, then
issymmetric
returns logical 0
(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 if A
is skew-symmetric.
More About
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
Since real matrices are unaffected by complex conjugation, a real matrix that is symmetric is also Hermitian. For example, the 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
Since real matrices are unaffected by complex conjugation, a real matrix that is skew-symmetric is also skew-Hermitian. For example, the 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, see Run MATLAB Functions in Thread-Based Environment.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
The issymmetric
function
fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray
(Parallel Computing Toolbox). 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™.
This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).
Version History
Introduced in R2014a
See Also
ishermitian
| isreal
| transpose
| ctranspose
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